Rainfall and Humidity
With some of the highest levels of rainfall in the world, you can expect to get wet and muddy. You can minimize the damage and discomfort by wearing quick-drying, breathable clothing made for high humidity trekking. Waterproof the seams of your tent and take extra waterproofing coating with you. Lay a water barrier under the tent before you put it up, and take an extra tarp to put over the top. Always put your campsite far away from waterways to minimize insect infestation and to protect against the possibility of flash floods.
Dangers and Precautions
The Amazon basin is one of the most beautiful and fascinating areas in the world, but it is also one of the most dangerous. Perhaps the greatest danger comes from the unseen. Tropical diseases, like typhoid and malaria, are real threats so get inoculations and medications before you leave on the trip. Another unseen danger is water quality. It may be tempting to drink straight from a stream that looks clean, but parasites are undetectable. Always boil water for at least ten minutes before drinking it. Because of the dangers of poisonous snakes, wear long loose pants and always be aware of where you are walking or reaching. Attacks by larger mammals like jaguar and boar are rare but possible. If confronted by a mammal, back away slowly and look downward to appear as if you are not a threat.
Regulations
Camping regulations vary from country to country so check with the regional national park system and the U.S. consulate for recommendations and precautions. Don't assume because no one appears to live in the area you are camping or that because there are no postings stating otherwise that it is legal or advisable to camp there. In addition to the possibility that it is private property, it may be a protected area. Most areas will have camping tours available, so when in doubt, join a tour.
Tips
You don't want to miss a minute of a trip like this, so make sure that you bring plenty of batteries for your camera since you aren't likely to run into a place to plug in a recharger. Since much of the Amazon basin is covered by a thick canopy, make sure your camera has a flash. Also, a pair of binoculars will come in handy too. Keep all electronics in waterproof bags, but air them out when possible to keep the condensation from the high humidity from ruining them. Take plenty of insect repellent and sunscreen as well.