I suspect /u/Jschooltiger may want to have his say for sure on this as well but there are several universal truths and very common methods. And that so long as a ship had any combination of sails, lines, and crew, she was never truly without her own propulsion systems!

On the first point we can state the somewhat obvious, that if the wind was cooperative a ship might get about under reduced or reefed sails. While smaller lighters, gigs, cutters and the like would skirt about under sail when possible transferring crew and goods as needed.

But if the anchorage was crowded, wind was down or in the wrong direction, or the distance to be traveled not very great, the ship might Warp or Kedging. Simply put this involved a portion of line fastened or wound round a fixed object such as a bollard. The crew would then haul in the line to get the ship moving and either cast off their end, or men ashore would do the same as the ship past and she would carry on her way. Kedging is similar but is done with the line to one of the ships own anchors. The anchor might be thrown overboard, or placed in a ships boat and rowed out some distance, then by pulling it in the ship will move forward as well. The classic 1956 version of Moby Dick has a reasonable enough depiction of the Pequod warping from the quay in Nantucket to give you an idea. https://www.youtube.com/watch?v=hdiFYCUP9oU

While finally if needs be men and oars could be used. Either off the side of the ship itself if small enough, or built for it. Or ships boats could be lowered to tow as needed.