Driftwood is expensive to buy at the store. If I find a piece of wood I really like, is it possible to make it into driftwood than can be safely used in my fish tank?
It's possible, what you're going to want to do is water-log the wood so that it sinks.
If it's a small piece, you can drastically shorten the time it takes to water-log it by boiling it constantly for one to three days depending on how hard the wood is. Once the wood is waterlogged enough to sink in water it's ready. Boiling it also helps to rid the wood of any bacteria and/or parasites that might be on it.
If the wood is too big to fit in a pot, you'll need a container that's big enough to hold the wood submerged in hot water. Unless you're able to keep the water at a boiling temperature, this process is going to be much slower, lasting several months (The natural process of water-logging wood takes about four to six months).
Submerge the wood in boiling water and let it sit. Every other day you're going to want to perform water changes, taking some of the old water out, and replacing it with clean, boiling water. As the wood sits in the water, it will release what is called tannins. The tannins won't harm anything, but it does make the water cloudy, so it's best to get rid of it as much as possible before you put it in your fish tank.
Depending on how you want your wood to look, after a week or so you should be able to start working the bark off. Taking off the bark should speed up the process a bit. If you want to keep the bark on, you'll still want to take a hard brush and scrub the bark to get as mush of the loose parts and dirt off as you can.
Keep doing the process of changing the water every other day, and scrubbing the bark once a week, for about two or three months. By that time the water should have seeped into the wood enough to make it sink. If it hasn't you can continue, or weigh it down in your fish tank if you want, by then there shouldn't be much more for tannins leaching into the water.
I prefer to avoid picking wood that's been in the water already. While it will give you a head start, you also have to make sure you don't bring along any hitchhikers (snails, leeches, small invertebrates). While it takes longer to water-log wood from dry land, simply submerging the wood in hot water should get rid of any hitchhikers there. If the wood you find is small enough to fit in a pot to boil it, then it shouldn't be a worry.
Some people suggest adding a tiny bit of bleach to kill the bacteria and hitchhikers when you can't boil the wood. The problem I have with this, is if you don't successfully get rid of the bleach it could seriously harm your fish, which is why I don't suggest it personally.
I've heard using saltwater helps (saltwater as in ocean water, not adding table salt), but I haven't tried it myself.
If I was able to at the time, I would have dropped a aquarium heater into the bucket to keep the water constantly warm. A broken heater that would keep the water boiling would be nice too.
To get the bleached driftwood look. You'll have to take off the bark, then bake it under a heat lamp for a couple months before water-logging it.
If you are creating your own driftwood, be very careful selecting wood. Avoid some processed, pressure-treated, or generally unknown wood, as they may be sprayed or injected with dangerous fire retardation chemicals or anti-wood-burrowing-insect pesticides. Processed planks with a line of green paint on them is a common indicator of such. These chemicals are so potent that no reasonable amount of tumbling, boiling, or bleaching can safely remove them. If such a material is used, it could potentially poison your tank either immediately or discretely over time.
Good thread on APC on what species of woods are safe.