I'd suggest two things;

Start looking for simplicity. Nothing over-constructed, but some small feature, maybe a well placed mound, that eithers causes you concern, or is deceptive, or maybe one you can use to aid in your attempt to acheive the goal at hand.

The other suggestionis to go into the bowels of this website, submerse yourself in the page long writtings and absorb.

Since one of the first things I learned reading these pages and getting insight from many of the practitioners is that everything is specific. Site, course, hole, shot, etc.

So where is that your playing this golf? Perhaps there is nothing of note to see, there.

For starters...

Consider imagining each hole in reverse.  From the hole toward the tee, think about the approach angles that reward the player with the easiest shot.  IMHO, superior architecture will always reveal a best route and sometimes choices of best routes to play the hole.  

Successfully negotiate/challenge a hazard and be rewarded, play it safe or fail in executing the proper shot, and be punished accordingly and in proportion with the miss.

Maybe over-simplified for some (and there are soooo many other things to observe and appreciate), but I think that's the most fundamental way to recognize the kind of shot-value thought that went into a course's design.  

Brent,
  What level of golfer are you?  Who designed the course the course you regularly play? What are some of the best courses you have played, and did you notice the architecture there?
   The downside to really delving into the architecture and learning more about it, is that it is really difficult to waste time golfing on mediocre courses, after you have seen some of the brilliance of the well-designed courses.

What level of golfer are you?  Who designed the course the course you regularly play? What are some of the best courses you have played, and did you notice the architecture there?

My handicap index recently dipped below 20 for the first time so I'm pretty much the prototypical bogey golfer. I'm a short hitter so whenever I score in the 80's it's a round where I hardly waste any shots around the greens. For me, the most fun in golf (well, other than knocking it close and having a tap-in birdie) is successfully making par on a long hole I can't reach in regulation. Hit the fairway, layup to a perfect distance right on a good wedge number, wedge it close and make the putt. I love that. I practice hitting wedges and chipping more than anything else because those are the shots I enjoy and I want to be able to hit them every time I need to.

The best course I've ever played in Pine Needles, a 36 hole day this past February. I can't explain a single thing that I noticed about the course architecture even though I loved the course immensely and can't wait to return when it reopens. The fact that I can't describe why that is the most fun course (by far) that I've ever played is what started my interest in GCA and brought me to this site. It's something about the green complexes that I like but without being able to describe it I'll just say that on that course (and to a certain extent at Mid-Pines and Granville Golf Course, my two other Ross courses) I can visualize shots that need to be hit around the green or even on the approach that I can't imagine when I'm playing other courses. It's like every hole has some kind of slope or contour that jumps out at you as "hit it here" and then it's just a question of executing the shot. Most courses are more like aim down the middle of the fairway, aim for the middle of the green, no real "options" seem apparent to me.

The downside to really delving into the architecture and learning more about it, is that it is really difficult to waste time golfing on mediocre courses, after you have seen some of the brilliance of the well-designed courses.

I disagree.

I can waste time playing golf on mediocre courses with the best of them.

I look at the routing and flow of the course carefully.  How the architect gets the round started and builds from there is important to me (I like a hole which introduces the player to the course; representative of what is to come, but not a round-killer nor a give-away- #1 at Sand Hills is a prototype; #1 at Black Mesa as an antithesis).

The angles from the tees and the location of the major design features (bunkers, green sites, surrounds) are of great interest to me.  Like most here, I prefer holes with multiple options, though I do not mind at all a hole or two out of 18 where the architect demands a certain shot (#17 at the TPC @ Sawgrass).

I am not a proponent of either pancake flat greens nor those resembling the Women's Putting Course at St. Andrews.  I like greens where you can see a variety of contours as you are approaching them, and which promote the confidence that if read and struck properly, that you can get the putt within three feet, and perhaps sneak in a few.

I look for holes which mix up the shots, e.g. a short par 3 followed by a long par 4 requiring a good drive and a mid to long iron.  Conversely, I don't like a difficult hole such as the long par 3 #8 at Cuscowilla, followed by a bear of a long uphill par 4, #9 (Coore supposedly does not like to follow up a long shot hole with a more simple one).

Variety of the hole within the one, two, and three shotters is important to me.  Particularly on the par 3s, I like the points of the compass concept, more so when 3 or 4 considerably different tee shots are required.  In areas where there are significant prevailing winds, I look at the long holes to see if they are typically downwind, and the short and medium length into it (which makes them play more similarly).  Likewise for courses on sloping topography- long downhill holes; short uphill ones.  I see nothing wrong with a drivable par 4 and a long one which requires a solid tee shot and a long iron/fairway wood second.

Holes that closely resemble others in the round either in the way they look or play are negatives.  Wild Horse has a couple of par 4s on the backside with cross bunkering falling in this category.   My home course, Great Southwest GC in Texas, has two par 5s and par 3s that play the same direction with similar clubs, and a few par 4s that are repetitive, which, in my opinion, greatly detract from what is otherwise a very good Ralph Plummer/Jeff Brauer course.

I also try not to read too much into the design of the course.  I am acquainted with enough architects to know that a number of the features are less the result of design intent than serendipity.  Nature, maturation, evolution, and cultural practices (Pinehurst #2) often account for some of the best things in golf.  In that context, I am generally in agreement with Adam Clayman's statement about simplicity.

A question that has been addressed here before but never to my satisfaction- can the average player really learn to see a course's architecture in a meaningful way if that person is unable to execute the shots?   Can the genius of Thomas's #10 at Riviera be recognized if the player can't drive it close to the green, or due to the velcro kikuyu preventing the bump an round, spin the ball sufficiently to hold the green with a wedge?  I am not trying to be provocative; just curious.
 

Actually, I think a truly great course engages all levels of play.  Some features will effect a twenty handicap and be unseen been by the two.  Conversely, the two finds interest in areas of the course the twenty may ever experience.  

Many designs overly depend on difficulty in an effort achieve greatness.  

If you play the course frequently (in other words, you're a member), try playing from all the different sets of tees.  This will frequently give you a vastly different perspective.

I'd also try playing the course by hitting to places off the tee you usually wouldn't 'visit'.  Try hitting to the outside of a dogleg to see if the architect is penalizing you.  You may find that the architect gives you a cleaner shot from out there than the shorter, but more difficult shot.

Try visiting some of the bunkers.  See what options you have - can you go for the green (from a fairway bunker), or should you play somewhere safe.

But my #1 way to 'do' architecture is to simply walk the course without any clubs.  Even better is to do this with another architecture fan.  See where the 'speed slots' are.  See where bunkers are designed to grab shots.  See where greens present optical illusions (take a ball for this one).  Make note of risk/reward.  See if the architect has built a fairly easy hole to act as a 'breather'.  Ask yourself if you'd change anything given the chance.

Dan H says- "But my #1 way to 'do' architecture is to simply walk the course without any clubs.  Even better is to do this with another architecture fan."

Agree.  And this is just one area where this site has substantial upsides.  I've had the good fortune to play and just walk a few courses with the East Coast Lefties (Childs and Cirba), and the things these long-time gca aficionados see and discuss are worth at least twice the price of admission.

One such example is the 8th green complex at Sand Hills, where I made two rather dumb bogies with decent tee and approach shots, by failing to notice the demands on and around the green.  In the post round discussions, Geoffrey and Mike brought up the neat green complex of the 8th hole (somewhat horseshoeing a mid-profile bunker).  Having to leave the course early next morning before the others in the group went out for another 36, I took a cart sans clubs for about an hour.   And thanks to the two Lefties and various other architecture veterans, I was able to see and appreciate what I missed on the previous day at the 8th hole and several other places.

From Redanman, I picked up on paying attention to the greens complexes and getting a feel for the break and speed of the chips and putts as you are walking up to the green (another reason to foresake a cart).  Not only does that allow you to see more of the whole picture as well as the detail as one gets closer, it also speeds up play.  Though I don't fully agree with Bill's observations on trees and eye-candy, specially bunkers without function, they are interesting and motivate discussion.

Tom Paul's maintenance meld, perhaps not an original concept, but one I have not seen made better by anyone else, is something that does not occur to many people.  So many of our better golf courses are not maintained in conformance to its design that the experience is greatly diluted.  For example, I loved Riviera, but that damn kikuyu detracts substantially from the way the course plays (particularly on holes 4, 10, 18).  I doubt that most people can see or appreciate the architecture of a course if it is not maintained in congruence with the design (a course where the topography is interesting, the major design features, and perhaps the wind dictate a ground game, but the course is maintained to allow only an aerial attack).

There are any number of other examples.  I particularly enjoy playing the classic courses with a knowledgeable, long-time member who shares the history of the place.  While the anecdotes are often perceptions and opinions as opposed to facts, it is interesting and uplifiting to hear how much people care about their courses and the game of golf.      

I pay attention to what the ball does after I hit it.

I also reflect on how many different clubs and how many different types of shots I hit during the round.

But then, I have never been much of a sight seer.

Michael,
   You have too much free time on your hands. I only get in about 25 rounds a year, and I don't take a single one for granted.

Brent,
  Lou brings up many good points. I think walking the course is a great way to see some of the architecture. I did this the first time I went to play High Pointe (one of Tom D's) early efforts. I took notes as I went around about features, contours, and green movement. The next day I played 36 holes and it was interesting to see what played the way I anticipated and what didn't. Then you learn a lot more of the subtlties as you go along with each round.
   Maintenance meld can be a HUGE issue at some courses. One I distinctly noticed a couple of years ago was at Barona Creek, out near San Diego. The first time I played was in January and the MM was perfect. The next time I played was for the first King's Putter, and at that time of year there is some other grass in play that causes the short game options to change. The springtime grass has a "sticky/velcro"-type quality to it that makes the short game more of a guessing game. So if I had played BC for the first time in the spring, I probably wouldn't have thought as much of the course, since I don't think the course plays as intended with that springtime grass.

Forrest- I was referring to the archtectural content, not all the slings and arrows hurled by the pety.

 Somwhere in those bowels are 5000 word essays, written with abundant sensitivity, by the man, who above said, he couldn't help with the subject. Now that's irony.

I don't know if all those perils of wisdom, made the cut to the new format, and I don't know how much Forrest has read of them, but If one can separate the wheat from the dis-jointed, there is plenty to absorb on many subjects. One of them is gca.

There was a demarcation line, and it was sometime just before the SI article hit the newstands.