Several manufacturers of polymer clay make gloss and matte glazes. These are brush-on finishes that dry in about an hour. Some glazes are water-based, which I have avoided, since they have a tendency to peel over time, particularly in pieces that have to withstand a lot of friction.
Another glaze I've heard that can be used is Future floor polish. This is actually an acrylic coating that works well on polymer clay. It is very thin, so to get the best shine, you need to sand and buff your pieces smooth before using it. When used on unsanded clay, it produces a finish more like matte glaze. You can also dip pieces in Future for a heavily-coated, very shiny look.
Many clay artists have also successfully used Flecto Varathane Elite Diamond Finish. This is a lacquer found in hardware stores, in the area with the wood stains and finishes. It comes in satin (matte), semi-gloss, and gloss finishes. A piece with Flecto on it can be re-fired for a stronger glaze. Flecto will also bend and flex without peeling.
Both Flecto and Future are much less expensive in quantity than the polymer-clay manufacturers' glazes. Since they come in large containers, you may want to put some into a smaller container for your workspace to make it more manageable.
Do not use nail polish to lacquer your clay, and be careful about using other glazes. Many lacquers - including most nail polish - will react with the clay over time, causing it to turn sticky. Some glazes, especially spray-ons, never dry properly when used on polymer clay. If you want to try a new glaze, make sure to test it first. You can try placing the piece in a low oven (200-250° Fahrenheit) for an hour or so; this sometimes sets a gummy glaze.
