
The fastest way is to enter your world seed into the interactive Pillager Outpost finder map on this page, which marks the exact coordinates of every outpost so you can travel straight to one. In-game you can also explore village-friendly biomes like plains, savanna, and taiga, since outposts are tall wooden watchtowers visible from a distance.
Pillager Outposts only generate in the Overworld, in biomes that can also host villages such as plains, desert, savanna, taiga, and snowy plains, plus some mountain biomes like groves and snowy slopes. They are semi-rare, typically generating every several hundred to a couple thousand blocks, and in Java Edition they never spawn within 150 blocks of a village.
Outposts are guarded by pillagers and a Pillager Captain; killing the captain in Java Edition 1.21+ drops an Ominous Bottle, which grants Bad Omen and triggers a raid when you next enter a village. A single loot chest at the top of the watchtower can contain crossbows, arrows, goat horns, and the sentry armor trim, and some outposts also feature caged allays or iron golems.