Some people might tell you to try on silver and gold jewelry to see which looks better, or even to think about whether you wear "warmer" or "cooler" colors normally, but the easiest way to find your undertones is just to look at the veins in your arm, because your undertones determine which color they seem to be. Are they blue-green? Then your undertones are warm! Keep in mind that most peoples' undertones are warm, so there's a high likelihood yours will be, in general. On the off chance, however, your veins are blue or purple-looking, congratulations—your undertones are cool.
Why is this important? It helps determine which makeup shades will be most flattering on you. If you have warm undertones, you'll want to select a foundation with more gold, olive, or peach pigments in it (Cover FX makes a whole line of products for specific undertones—their Cover FX Total Cover Cream Foundation is a longtime movie set staple, and their shade selection is excellent).
If you have cool undertones, you'll want a shade with more yellow-pink tones in it (typically, very fair and very deep skin tones are more likely to have cool undertones, and Nars Sheer Matte Foundation has very good options for people who are on both farther ends of the spectrum).