There are three aspects of rainforest photography that must always be kept in mind; 1) it is very hot and very humid in tropical rainforests, 2) it is dark in rainforests, and 3) there will be lots of neat things way up in the canopy that you will not be able to photograph, and things you will hear but never be able to see! Frustrating but fun!
In the "good old days" of film photography, the heat and humidity could sometimes cause the shutter mechanism of a camera to slow or simply stop working. Digital cameras do not have this weakness, BUT - moisture is the enemy of anything electronic. There are obvious tools to use, such as a small umbrella carried in the camera bag to hold over the camera to shoot in the rain, but more subtle than the threat of rain is that of the humidity. If you take a camera out of an air-conditioned room into a hot humid environment, moisture will condense not only on the outside of the camera and lens, but possibly inside as well. A simple solution is to keep you camera and lenses in an air-tight case, and allow time to adjust to the heat before opening the case. If you have an air-tight case, load it up with moisture-absorbing packets before your trip. A more simple approach is to keep your camera and lenses (and flash) inside sealed Zip-lock bags for a few minutes when leaving a cold room. It is OK to take them directly from the heat into your cool room - let them cool down and any moisture evaporate before putting them back in their Zip-lock bags.
It is dark in the jungle! Look for shafts of light landing on flowers or insects to find interesting contrasts. Always have your flash, and realize that without a powerful flash you probably will not be able to photograph those birds and monkeys (especially the ones that are moving!) that you see 30 feet in front of you! Plan on using your flash a lot - take extra batteries! Remember the value of fill-in flash. I found the monkeys below with very bright diffuse light behind them and used fill-in flash to get this photo.
In clearings in the rainforests look for flowers - you will be able to find a large number of butterflies and hummingbirds in these clearings. Toucans, oropendulas, and other interesting birds may be nesting or hanging around the edges of the clearings, so these can be good spots to see them.
There are lots of great butterflies and other insects and bugs in the rainforest, so don't forget macro photography. Going out with a good guide is always helpful - "There's a vine snake" our guide said, pointing. I looked into the forest where he was pointing - focusing about 8 or 10 feet away. "I don't see it" I said. "It is about six inches in front of your nose" he said! "Ohhh - THAT vine snake!"
Shooting with a hand-held long telephoto can only be done with LOTS of light!
In cloudy conditions, and most certainly in the rainforest, the only way to use a telephoto is with a tripod. And although image stabilizing technology is good, always plan on having a tripod or at least a monopod with you if you are bringing along a telephoto!