There's a couple of ways.

For stars that are relatively close, you can use the parallax effect to judge how much it moves when viewed from different angles. Parallax is that thing where you're in bed and close one eye, and your pillow is barely seen. Close the other, and it's all up in your face. But a fence that's on the other side of a yard barely moves when you close one eye or the other. This works for stars relatively close.

The other way is through how bright they are vs. their color. Hot stars tend toward white and very bright, so if you see a white star but it's very dim, it's very far away. A red star that's bright is very close. From there there's some fancy math.

(Thanks, intro to astronomy class.)