Use your best telephoto and macro lenses. Some little creatures wont allow you to get very close and since you don’t want them to be scared away and chase them all over the place for a long time, you may consider a telephoto lens.
Be very patient, move slowly and silently. Try again and again; don’t get angry because this is one of the subjects that are hard to get right from the first time. They move fast and unexpected.
Surprise your little bug in the middle of an interesting action (like feeding time, reproduction time, fighting, and so on).
Know with what you are dealing with. Maybe its a deadly spider, maybe its a friendly butterfly that will even settle on your camera. Also, learn their habits so that next time you encounter that creature, be prepared to shoot better.
These creatures are usually very small meaning that the camera will hardly find the right focus point. I suggest using manual focus (set it to the minimal possible distance when you can get close enough – about 3-5cm).
Try every angle: front, side, above. Study the physiognomy of your subject without interfering with it. Don’t touch it (supposing you could do that), let it stay and do whatever it desires. Of course, don’t kill it: you are a photographer not a bug criminal.