(this page is written from a backpacking perspective)
Wood fires burn hotter than charcoal fires, so food often comes out burnt on the outside and uncooked in the middle. There are several ways to deal with this problem:
Use a heavy cast-iron pan or dutch oven. The large metal mass helps mediate the heat. But obviously these pans are too heavy to use when backpacking.
It's important to maintain the fire correctly. The wood goes from flame ⇒ coals ⇒ ash; you want to accumulate a good bed of coals.
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Use hardwood not softwood, because it burns longer and cooler.
The Zebra brand is very popular, however, billy cans originated from cheap DIY cans. (since they get all sooty, you may not want to spend a lot on them)
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Many tea kettles work as-is, since they normally come with handles.