1. As John says, don't take pictures while you're playing -- or at least, don't expect them to turn out well. It is almost impossible to play well and take good pictures at the same time, so you should enjoy playing when you're playing.
2. The best time to take photos is two hours after sunrise and two hours before sunset, when you've got some shadows to help see the contours and add depth. Maybe a bit more than two hours on a tree-lined course; maybe even later on a totally open links course.
3. With maybe a few exceptions, of the thousands of really good golf course photos I've seen, nearly all of them have the flag for the hole in the picture. Without it, people have a hard time orienting themselves or understanding the hole. If it's breezy, the flag will appear bigger or smaller based on how the wind is affecting it, so if you've got what you think is a great photo, take several pictures in succession, and sort later for the one where the flag is most prominent. [In the old days of film, you would also take slightly over- and under-exposed shots to get the perfect lighting, but now that's all done by software.]
4. How you frame a photo, according to Charlie's rules in the last post, is very important. Some people are very good at composition without trying; others will always struggle with it no matter how much you try to teach them. Look at some of the pictures you've taken, and see where the flag position [or the golfer] was in the picture, vs. the rule of thirds, and you'll know if you're a natural or not.