Summarize:

Even in small worlds, finding one village amidst tens of thousands of blocks is a bit like finding a needle in a haystack. Villages spawn in Desert, Savanna, Taiga (including cold variants of Taiga), and Plains (including icy plains) biomes. If you find yourself in a Jungle, Mushroom, Tundra, or other biome not supported for villages, don't waste your time looking. Villages are often made of wood planks and cobblestone, and tend to stand out from their surrounding areas. It can take hours to find a village, so stock up on basic tools, a bed, food, and weapons before you set out. It's best to travel during the day and camp during the nights, so consider digging yourself a hold and sealing it most of the way to keep out mobs. You'll need to leave at least one block open to avoid suffocating. If you happen to have a saddle, you can use it to get a mount and speed up your exploration. Find a horse and interact with it several times with an empty hand until it doesn't throw you off, then sneak up to the tamed horse and select it with the saddle to make it controllable while you ride it. Navigate to the tallest hill that you can find in a biome in which villages spawn. This will allow you to take in the surrounding areas, making it easier to spot man-made structures. You'll be able to see fire much more clearly at night than during the day. While fire at night may be lava, there's a good chance that the fire is coming from torches—and torches typically mean villages. Be extremely careful while doing this if you're playing survival mode on anything other than "peaceful" difficulty. It's best not to investigate the torches until the following day due to mobs. Villages are random, and there is no sure-fire way to find one in the game without using third-party tools. For the best chance at finding a village, take the time to explore each compatible biome you come across.
Understand that finding a village may take hours. Know where to look. Know what to look for. Prepare for a long journey. Tame a mount for transportation. Find a viewpoint. Look for torches at night. Keep exploring.