Summarize:

If you're really familiar with snakes, and you know that what you've caught is a garter snake or another nonvenomous snake, you might be able to get away with touching it. But if you're at all unsure what type of snake you've caught, don't take the chance. Wild snakes don't much like to be handled, anyway. Gently carry the entire trap to your vehicle and put it in the trunk or another enclosed area so you can transport it.  Don't shake the trap or poke at the snake. Handle it with care. You might want to keep small children and pets away from the trap while you're handling it, just to be on the safe side. If you let the snake go too close to your house, it will find its way back to its home territory. Release the snake at least a mile from your home if you want to make sure it doesn't come back. However, if you trapped the snake in your house and you don't mind if it lives outdoors in the yard, you can just walk outside to release it there. The snake will have the best chance at surviving without disturbing other people if you release it in a natural area. Go to a state park or another area without a lot of people living close by to release the snake. This way it won't end up in someone else's garden. Freeing a snake is not usually dangerous; in most cases, the snake will be happy to slither away and leave you alone. But just in case, wear long pants and gloves when you're freeing the snake. Watch the snake carefully and be ready to move out of the way if it decides to strike. Depending on which kind of trap you used, there are two different ways to free a snake:  If you used a reusable glue trap, unlatch the lid of the box and open it up. Pour vegetable oil over the snake's body, making sure to cover the entire are that's attached to the glue. The trap is designed so that the snake will be able to wiggle free from the glue once the oil gets between the snake's skin and the bottom of the trap. By this time you should be standing a fair distance from the trap so you aren't blocking the snake as it leaves the scene. If you're using a minnow trap, put on a pair of heavy gloves, since you'll have to get a bit closer to the snake (though you still won't have to touch it). Carefully open the two sides of the trap to separate them at the middle. Leave just enough space for the snake to crawl out. Move away so you aren't in the snake's path when it crawls out. All snakes, even venomous snakes, play an important role in their ecosystems and should be released if possible. But if the snake is venomous and you're concerned that someone could get harmed by it, you killing it might be the answer.  If you used a cardboard glue trap, you can just put the whole thing in a garbage bag and seal it up. If you use a minnow trap, you can place the entire trap underwater for a few hours before opening it.
Don't attempt to touch the snake. Drive at least a mile from your house. Go to a natural area without many residences nearby. Free the snake. Kill the snake only as a last resort.