The sails can rotate around the mast, and are controlled by various ropes; typically one on each end of the yard (post along the top of the sail) and one on each of the bottom corners.
So all the sails are rotated to be at about 30 degrees from the centreline of the ship (so 60 degrees from being athwartships). This means that with wind blowing from about 50 degrees off the bow the wind “sees” the back face of the sails, and they pull the boat forwards. Or rather they pull the boat mostly sideways and slightly forwards, but the boat is bad at going sideways and good at going forwards so it only goes sideways a little bit which is called leeway.
If you look at the yacht “Maltese Falcon” you can see how a square rig is not so different from a single modern sail.
As for going from one side to the other as another commenter mentioned this is called tacking, and in the moment when the boat turns through the wind she is being blown backwards. Luckily boats have lots of momentum so in most conditions can get through the wind onto the other side without stopping.
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