Larger ships rarely sailed directly to the pier when they docked. While they might have a minimum of sail to have speed enough to navigate when aproaching the pier, the last stretch was usually manually handed, by warping.

This means that the ship stops and the anchor of the ship is put in a boat and rowed to the position the ship want to take. The anchor is then dropped and the ship can pull itself to the anchor by raising the anchor until it is in the position it wants to be.

Another way would be to sail at a very low speed until the ship was close enough to throw lines to men ashore, who would then pull the ship the last distance until it could be tied up pierside.

Hi! There have been a few posts on docking that you may find interesting. Not discouraging further discussion here, but you can get started on these:

• During the age of sail, how did large ships maneuver in ports? - featuring /u/DBHT14 and links to several other posts

• A Few Historical Sailing Questions - more detail from /u/mormengil

These posts are all archived by now, so if you have followup questions for any of the users, just ask them here & mention their username to notify them

Large ships approached docks slowly, using the various techniques described in the answers linked by u/Searocksandtrees, and summarized by u/vonadler.

However, there were a few other factors which helped them avoid damage when coming in to dock.

One factor is that the displacement of the water between the ship and the wall of the dock acts to some extent as a brake. Water is in-compressible, so the water between the side of the ship and the side of the dock needs to be moved out of the way (flowing under the keel, or around the bow and stern). The energy needed to move this water slows the ship down as it gets closer to the dock.

"Fenders" would also be deployed between the ship and the dock. Fenders are designed to deform (squish), to absorb some of the energy between the ship and the dock, and also to spread the load of the impact between ship and dock so it does not concentrate on one point and cause damage. Fenders are made of inflated plastic, or foam, or rubber (old tires are often used), today, but back in the age of sail were often made of a heavy rope covering stuffed with fabric (old rope, for example). Fenders, hung off the ship, and / or the dock, provided a cushion and prevented damage as the ship came alongside.