What is cunnilingus?

Cunnilingus is the fine art of making love to a vagina with your mouth and tongue. It is a delicate skill, requiring patience, practice, and dedication to get it right, but any woman you learn to do it right for will appreciate you all the more for it.
What applies to the penis applies to the vulva-- every one is different, requiring a different touch to make its owner happy. But few tools can equal the tongue for the amount of pleasure it can deliver to a happy vagina.
This article assumes that you know what a vulva looks like and can identify with some precision the mons veneris, labia majora, clitoral hood, clitoris, labia minora, urethra, vagina, and perineum, to name them (approximately) from top to bottom.

How fast should I go?

This isn't an attack. Don't go after the clitoris like a fireman attacking a fire. Quite often at first, the clitoris is far too sensitive for direct stimulation. Lick around it, stimulating the hood, teasing her inner labia, tasting her. Take your time and listen to her. Some women make noise, and some do not. It will be a while before you learn exactly what your lover prefers as far as oral sex is concerned.
Some women may like additional stimulation-- a finger or two into the vagina, or perhaps even the anus. She may want your hands to reach up and play with her breasts, or she may want your fingers to hold her labia apart so that your tongue can get at her vulva more directly.

I've heard cunnilingus doesn't taste good.

If the taste or smell bothers you or is a concern, ask her to wash first. Most people who enjoy cunnilingus agree that a clean vagina is a good, if acquired, taste.
As a woman nears her climax, she may want more direct stimulation. In general, fast, rhythmic stimulation is most effective at causing climax-- but there shouldn't be a rush to get there. Take your time and learn to appreciate what you can do for her.

What about cunnilingus during menstruation?

Some people are particularly turned off at the suggestion of cunnilingus during menstruation. If it is a concern to you, then wait. A tampon may well hold the blood back, as will a diaphragm, but some men can't stand the taste anyway. If your partner is healthy, however, there is no particular danger in menstrual blood, and some women find that orgasms during their periods allievate cramps.