Anyone who's taken a motorcycle training course knows the answer. To make the bike turn right, you push on the right side of the bar. Then the bike leans to the right and turns to the right. Pushing on the right side of the bar turns the tire to the left.

If you don't apply pressure to one side of the bar or the other, it will go straight, all by itself.

The problem with bicycles is that it requires so little pressure to make a turn, that it's not obvious what's going on. I've done high speed turns on a mountain descent, using only an open hand on the hooks. Push on the right side to turn right. Quite pushing and the bike straightens up, all by itself.