Regarding mechanical advantage haul systems the most commonly known and used are the 3:1 "Z-drag" and the 4:1 "Pig (for piggyback) Rig". It is pretty easy to find tons of videos and on-line tutorials for how to set up either, but there are few good videos showing them in use in a real life, unstaged situation.
In 2013 I attended a swiftwater rescue symposium held by the ACA on the Tuckasegee River in North Carolina. The instructors included some of the "superstars" of swiftwater rescue including Charlie Walbridge, Les Bechdel, Slim Ray, Sam Fowlkes, Jim Coffey, and many others. Below are a couple of links to videos that someone took at a couple of the presentations.
Often the most difficult part of using a mechanical advantage drag or any rope system to rescue a pinned boat is what is often called "rigging the boat". When the boat is pinned in swift current it is often very challenging to safely approach it close enough to secure a haul line and a tag (control) line to the boat. Multiple attachment points dynamically rigged to distribute the load is always preferred since grab loops, thwarts, and yokes are often easily torn out, especially when using a drag system that incorporates mechanical advantage. In the first video big Walter Felton from Arkansas shows some techniques for rigging lines to pinned canoes and kayaks, as well as a very simple vector pull technique using only ropes that can be applied in scenarios where prusik loops or cords, carabiners, and pulleys are lacking.