When applying varnish, sanding between coats is a common practice. Sanding with very fine-grade sandpaper -- 400-grit or higher -- removes imperfections and smooths raised wood grain to make the finish perfectly flat and level. Ideally, you should never have to sand down the final coat but you may have to if the varnish hardens to an uneven surface. If this happens, gently sand the varnished surface down until it is perfectly smooth. Don't worry about the micro-scratches -- those will get buffed out later.
You need different cloths for the sanding and buffing processes. For sanding, a tack cloth is ideal for getting rid of the dust you create, but you can easily substitute that for a damp cotton cloth, which works just as well to collect wood dust. During the buffing process, you may use either a soft, lint-free cotton cloth or a microfiber polishing cloth to apply the rubbing compound and polishing compound. You may also use a hand-held buffing pad to buff the compounds into the wood.
Compounds designed for buffing out scratches on automotive finishes are commonly used on wood surfaces. Automotive rubbing compound will fill in all of those micro-scratches you created during the sanding process. As you buff, the scratches will slowly disappear and the finish will start to shine. Avoid focusing on any one area -- this can create an uneven finish. Start with a small amount, and then add more rubbing compound as necessary. Keep buffing in small circular motions until the scratches have disappeared.
Once you've buffed out the scratches, you may find that the wood is shiny enough without having to polish it any further. However, if you decide that the finish could use an extra bit of shine, you may use standard furniture polish with lemon or orange oil, or continue using automotive products and stick with a polishing compound. As with the rubbing compound, start with a very small amount and buff in tight circular motions. Add more polishing compound as necessary and buff until the wood is glossy but feels dry.