People who've golfed with me say they've never seen someone make so many long putts and miss so many little ones. I feel like I can really read and feel greens well which lends itself to making more than my share of long ones, but for the short ones which, in my opinion, are more a matter of technique and repetition, I still need to do some work (and possibly look into a labotamy). I've never really put my method of reading greens into text, so please bear with me and forgive my rambling, long-winded tendencies...
I guess I'm a bit different in that I don't separate line and speed until just before I step up to address the ball, and then it's only for the purpose of simplifying things in my mind. Line and speed to me are not really two separate entities since what you're really talking about in both concepts is slope. I'm trying to get the feel of the overall area of the green that encompasses the putt, and not just the exact line on which the ball will travel (depending on severity of the slope this is usually maybe a 10 or 20 foot wide alley beginning behind the ball and extending past the hole). When dealing with a new course I try to get an overall feel for the terrain the green is situated in and then work my way down to the whole green and then smaller area surrounding the path of my putt (that alley concept).
This comes with practice, but on courses which are unfamiliar, you can do little things to get a feel for the greens without doing the Tiger-stalk. Walk around them as you set your bag down, thinking a lot about how the terrain feels to your feet and how that matches up with what you're actually seeing. After awhile this will become instinctive as you reach every green and you won't even really notice you're doing it.
As the picture of the putt becomes more concrete in my head, I crouch behind and try to narrow that feel down even more, do a quick visualization of the path I want the ball to take and how fast it will look like it's going, and as I move into the phase of addressing the ball, I pick a spot on that path that's only a few feet in front of my ball. This is where I separate line and speed. In my mind I'm already committed to that putt since my reading is finished - I do not do any more reading once I'm over the ball unless I feel something that *really* contradicts what I've already felt/read on the putt. In my opinion, I can do a lot better job of obtaining the feel and information in the feel-gathering phase and when it comes to the address position I've got to trust what I've read. Second-guessing at that point results in tentative strokes and terrible putts.
I square the putter and my stance to that point in front of my ball, commit to that line, and then focus entirely on making the picture I saw in my mind of the pace of the putt come to fruition. From there it's a matter of using sound fundamentals (ie accelerating through the ball and other technical aspects which should be second nature through practice) to bring the mental picture of the putt into reality.
For such a simple question you posed I had to do a lot of reflection of what I actually do on the greens to put it all into words. In lessons I usually am teaching more about the technical fundamentals and get the feel aspect across by emphasizing the importance of practice, of getting onto as many different types of greens as possible and experiencing all the different slopes and distances so that all of your different senses can train themselves. The greens I play most often are Langfords, which are a blast if you're as much of a feel putter as I am. Mike DeVries's greens appear similar in terms of the dramatic slopes and contours, and I look forward to learning and comparing and contrasting them in terms of how they actually putt.