It's important that before you get to the buffing stage that you gradually wet sand the finish to a pretty fine point, and you can't skip steps. Each sanding stage removes the scratches from the previous stage and if you try to skip one, you'll end up not removing the deeper scratches from the previous abrasive. Once that happens, everything you do after that is almost a waste of time; it'll never get to that "wet glass" point you're looking for.
You also have to be patient about letting the finish harden, or it won't respond properly. Too soon, and all you'll do is load up the paper and not get much work done. You also need a good hard rubber backup. Trying to do it with just paper in hand will leave you with a wavy surface.
When I did the L5S, after two weeks the finish was ready to abuse. I started with 600 grit, and gradually worked through 800, 1000, 1200, 1500 and 2000 grit papers. At that point, it was ready for buffing. I used StewMac's
Colortone compounds, just using the medium, fine, and swirl remover grits. Those I applied with with a Makita 9227C buffer...
That unit has the hook & loop pad attachment Tonar mentioned. Allows for easy changing of the pads. I used wool; foam works too.
Be sure to get a pad for each compound! You can't change compounds on a pad, or you're wasting your time. Get to the finer grits, and you'll still be rubbing in the coarser grits, which is defeating your purpose. Finally, some Meguiar's Ultimate Liquid Wax hand applied & rubbed out. That got the finish to this...
Be sure to apply the compound to the pad, not the work surface. Also, cut a neck and armholes out of a garbage bag to wear as a shield, and don't do this near anything you wouldn't want to get rubbing compound on. The stuff flies, and I'm not kidding.