To do it right:
If the slide is rough or beadblasted:
Get a good grade of metal finishing paper in very fine grits, and some crocus cloth.
Buy a piece of thick plate glass at least 6 inches wide by 1 to 1 1/4 foot long.
Get some rubber cement, and starting with the coarser grits, glue the paper to the glass.
Lay the slide flat on the glass, and holding a firm dow pressure, push the slide across the surface. Don't "rub" back and forth, just push away from you, in one direction. Every few strokes, turn the slide around so you keep the polish equal.
When you can see only a grained surface with no other scratches, remove the paper, clean the glass, and glue on the next grit paper. CLEAN THE SLIDE EVERY TIME YOU CHANGE THE GRIP PAPER. Use a solvent for this.
Continue until you've worked your way through the crocus cloth.
Brownell's sell VERY fine grit cloth which is much better than that found at the hardware store.
The final "mirror" finish is put on either with a motor and wheel, using polishing compound, or can be done by hand with cloth and compound.
This doesn't take as long as it sounds, and unlike power buffing ,
there is less chance of rounding off sharp edges, or dishing the flats. It costs less too.
The only cautions are making sure not to bear down too much on one end or side of the part, making it look unequal, and be sure not to begin removing the slide serrations and lettering. The object is to POLISH, not remove metal.
If the slide is "normal" stainless:
Get a piece of old blue jean and some metal polish. Glue the jean material onto a strip of wood around 1 foot wide by 3-4 inches wide. Coat the material with polish, lock the slide in a padded vise, and holding the wood strip with a hand on each end, push the center of the strip down the length of the slide. Stay away from the slide serrations.