Oooh my specialty! (I'm an Excercise Physiology major so we spend all day studying the effects of excercise on the body.)
I haven't been to the gym much recently, but that is because of winter break and joining the hockey team (I'm sore enough from hockey 3 times a week that the gym would be overkill (although I do need to get back for some strength training)).
Anyway, you didn't really say what you do at the gym...
When I go, I stretch for maybe 10 minutes, then jump on an eliptical machine for 10-15 minutes. Then I usually do the nautilus machines until I'm either my muscles are finished or I'm out of time. When I'm doing what I should be doing, I'll have saved 10 minutes for a cool down stretch, but usually I don't.
I don't know exactly what you do, if it is a class or swimming, then I wouldn't worry too much about it because it is hard to over exert yourself swimming and in a class there is a trained professional there to tell you if you are doing something where you might injure yourself.
If you are doing something on your own (like what I do above), it is important that you know the right way to do excercises because you could get injured otherwise. If you can, your gym might offer something where someone can walk you through a routine once or twice and show you the right way to stretch and use certain machines. Or if you can't do that (it probably costs at least a little money to do that) you can look up most of the excercises online.
Anyway, forgive me if I got a little preachy, it is sort of something that I'm passionate about because excercise can be so much easier than people make it out to be. With a little practice, it just becomes part of your life and you won't even really notice when you pick up your gym bag on Tuesdays.
