It is called tacking, you can alter how the sails “catch” the wind, so can push you from side to side rather than in a single direction Sails actually work best when the wind is on the “quarter” rather than directly behind them so all the sails are being pushed. By tacking you can slowly in general head into the general wind direction, but never moving directly into the wind.
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.
Imagine the sails being rotated 45° and the ship sailing at right angles to the wind. No problem, right? So why not allow the sails to rotate a little farther and then the ship can turn a little closer to the wind. Square riggers can’t get much closer than 60° off the wind at best, unlike modern racing yachts which can make it to 45°, so square riggers can only make very slow progress into the wind. Mostly they relied on knowledge of prevailing winds in different regions and at different times of the year to minimise the need to sail upwind.
As others have pointed out, the square rigged sails can be rotated to catch the wind, but a square rigged ship would also be able to put up sails that run along the centerline of the ship as well. They would typically have a large boom on the mizzen mast for a sail called a “driver” (also called a spanker). They could hang several triangle shaped sails, called jibs, between the foremast and the bowsprit. They could also hang triangle shaped sails running fore/aft between the masts called stay sails.
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