xkcd

Edit: I have been corrected. Please read the follow-up comments for better information. I'm leaving the original text below for context and transparency.

As I understand (I'll happily be corrected), the basic mechanism is that you want to align your ship diagonally off to the side, and the sails at a shallow angle so that the wind pushes you to the side (diagonally back and to the side, but the hydrodynamics of your bow resist the backwards component), so you gain some momentum. Then you turn into the wind to have that momentum carry you forward, sails parallel to the wind so it doesn't push you back as much. Turn off to the side again (either back to the same side, or continue your turn to the other side) and repeat.

It doesn't move you quickly, because it's rather inefficient in transferring the wind's power into opposite momentum, but it gets you moving at least a little.