I often stain shelves, furniture, etc. and am not pleased as I would like to be with the final finish. I usually apply two coats of stain and follow that with three coats of polyurethane. I sand lightly with 220 sand paper between each coat of poly. The final finish is acceptably smooth but not as smooth as commercial furniture. What do I do to take it to that final level of smoothness?

most commercial furniture is usually finished with laquer because it dries quickly and finishes relativly smooth. any roughness is cleared up with wet or dry paper with grits as high as 600. Of course they are in a climate controlled enviorment with controlled humidity. which you can't get at home, unless you live in a dry state like arizona ( dry as in humidity, not booze )
You might try spraying with a suction feed , exterior mix spray gun, that will help some. as well as using a finer grade of paper. You can also try automotive polishing compound , both red and white, with white being the finer grit, after which wax with a paste waxsuch as johnsons pastewax

in addition to that I use fine steal wool to apply the paste wax.