How did people tell which direction was south and north before the invention of the compass?

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Zither13

If you face the setting sun, north is on your right and south on your left. Thus the term southpaw for left-hander.

Compasses only give you magnetic north and south. This, and a few handy constructions, give you rotational poles.

As for pole stars, sometimes we have them and sometimes we don't. We are moving towards "don't." The celestial pole will move away from Polaris after the 21st century, passing close by Gamma Cephei by about the 41st century. In the ancient world, the pole was close to Thuban around 2500 BC. During classical antiquity, it was closer to Kochab. It was about the same distance from either Kochab or Polaris by the end of late antiquity. Pytheas, around 320 BC, described the celestial pole as devoid of stars.

Polaris could reasonably be described as stella polaris from about the High Middle Ages.

Mamertine

They used the stars. In the northern hemisphere Polaris is always to the north. In the southern hemisphere it's a bit more complex as there's no singly identifiable star right over the pole but you can still find south by the stars.

Also the sun (and moon) always rises in the east and sets in the west. Depending on the season and hemisphere it does rise more north or south from true east, but again it can be used for navigation.

Searocksandtrees

Looking at the etymology of the English words provides a clue for cultures that use languages from the PIE language family:

The word east comes from a PIE word meaning shine, as in dawn, referring to the direction in which the sun rises. West comes from evening, as in the direction in which the sun sets. If you "orient" yourself to face east, north is everything on your left, while south is the sunny side (which obviously makes sense only if one is in the northern hemisphere).

Here are some other posts on directions and navigation