Instructions
Buy boots from vendors. This is the most reliable way to find a good, sturdy set of boots. The odds of finding a rare pair of boots at a vendor is fairly low, but if you're walking around barefoot and just need some good leather on your feet, a vendor is as good a place to start as any.
Kill monsters. Monsters often have a chance of dropping random items, including footgear, when they die, along with the money they usually also drop.
Open chests whenever you find them. Chests are rare and hard to find, but usually contain at least one good item --- and sometimes, it's boots.
Trade with other players. Often other players will have a spare set of boots taking up space in their inventory. If you can pay money or trade other items of value for another player's extra or castoff boots, many people will be happy to pass them off to you. In a safe, public place, find someone who's wearing better shoes than you, then ask her whether she's got another pair she'd consider selling to you. You may not find a seller on your first try, but sooner or later you'll find someone who's just been waiting for you to come by, and you'll end up with a nice new pair of boots worth the wait.