Approach the mooring from downwind or against a current. Note how other sailboats are lying (such as the one moored ahead in this photo). Use the wind or current to slow your approach.
Well before reaching the mooring, have a crew ready at the bow with a boat hook. Even if the mooring has a pickup buoy with a pole that reaches deck height (called a mast buoy), it’s good to be prepared with a boat hook in case the wind, waves, or a current moves the sailboat before the crew can reach the pickup.