The boat turns about the centreboard, in the middle of the boat. You can think of it as if the boat is hanging on a string tied to the top of the mast. If you push the front away from you, the back will turn towards you. If you push the back away, then the front will turn towards you.
Sitting in the normal position, with the wind coming over your shoulder and the boom over the other side of the boat, you push the tiller away from you to steer the boat closer towards the wind, because this pushes the stern away from the wind, turning the bow towards the wind.
There are Three ways to make the boat turn.
Away from the wind
Towards the wind
With the rudder.
Pull the tiller towards you and the boat turns away from the wind.
Push the tiller away from you and the boat turns towards the wind.
With the Sails.
Pull the front sail (jib) in tight and let the back (main) sail flap and the boat turns away from the wind.
Pull the main sail in tight and let the jib flap and the boat turns towards the wind.
By letting the boat lean.
If you make the boat tip (heel) towards you the boat turns away from the wind.
If you make the heel away from you the boat turns towards the wind. This is what will happen if you let everything go.