Learn the macro settings, if your camera has them. Most digitals do now. You need macro if you want those close-up shots. It allows the focal point to be much closer to the lens, which in turns allows you to shoot much closer to the fly.
I had a Nikon Coolpix 5700 that had the option of using additional filters or lenses on an optional tube sort of thing that went over the lens. Some digital point-n-clicks have this option, though most don't. If yours does, then great. Get yourself some diopter lenses (they are pretty cheap on eBay). They will allow you to put the fly right up to the glass, and it adds a magnification factor as well. You can get shots like this no problem:
The only problem with "fake" macro photography with point-n-shoots like this is the depth of field is extremely shallow. The f-stop doesn't go down far enough. With flies it's really no big deal, you're only normally shooting on one plane anyway. With more 3D objects, it's a much bigger problem. True SLR cameras with very large apertures will solve this problem for you. You can see how shallow it is in this pic:
The more magnification you use, the shallower the DOF gets.
Make sure to use a good flash, too. Normally the built in flash of the camera sucks. If you can, get a remote flash of some kind, or just light the fly with some very bright lights. A fash shutter and a large aperture will give you very crisp close-ups.