Inspect Mount
One of the most important parts of hammock camping is ensuring proper placement. Make sure that neither of the trees you stretch your hammock between are dead. Dead trees are much more likely to snap or collapse. Another important consideration is dead fall, or dead branches that become stuck in live branches. A high wind can knock these dangerous branches loose. Make sure nothing likely to fall hangs above your hammock location. Finally, be sure to pick trees that are over 6 inches in diameter so they can bear your weight.
Inspect Equipment
Make sure your equipment is up to the task before each hanging. Inspect the webbing you use to wrap around the anchor trees. Look for fraying or other wear-and-tear. Check the locks on your carabiners or metal connectors. Never allow pressure to be applied to the gates of a carabiner. Finally, check the hammock itself for signs of tears or stressed seams.
Proper Equipment
While your camping hammock is designed to hold a human, you're other equipment may not be. Webbing, used to tie off around the anchor trees, is typically load-bearing. However, rope, which you may need to provide a little space between your anchor and your hammock's attachment point, is not always load-bearing. Make sure to only purchase rope that can hold your weight and then some, since tying knots in rope can significantly weaken its structural integrity. Carabiners are another item which frequently are not designed for human loads. Make sure your carabiners or other metal connectors are designed for climbing purposes.
Environmental Considerations
Hammocks are not as well-suited to cold weather camping as tents. The weight of the human body on the hammock tends to crush sleeping bag insulation, resulting in a cold surface and discomfort. Make sure to bring a rain fly or tarp that can be easily tied above the hammock. Finally, hammock users, being out in the open, are far more subject to insect bites. Make sure to bring mosquito netting or purchase a hammock with built-in netting.