Answer: just put your tongue in her pussy and move it wildly in all different directions.
The previous answer given is a vague one and it does work but isn't very good and is only for pure amatures. If you really want to be good and get her screaming or moaning and feeling GREAT, then heres what you do:
First after you've done your romantic stripping of her and yourself (if this is forplay for sex, if not then you'll only have her pants down) you begin to kiss the upper half of her inner thighs being sure to get them wet. start halfway up on one side, then when yourr almost at her vagina, switch to the other. this is for teasing purposes. once u reach her vagina on the other thigh blow air on them. this will be realy cool on her thighs and help arouse her even further.
now she should be nice and wet, so put your mouth extremely close to her vagina and breath your hot breath on it. She should like the feeling and most likely arch her back ultimately forcing her vagina to your mouth. if she is too timid for this you can just begin on your own. Many people say to start slow, but surprise is all part of the arousal process, so dive right in! just put your mouth up to her vagina and begin moving your tongue up and down inside the labia (in layman's terms, her pussy lips) then when your ready you can stick your tongue inside and move it around or in and out. MAKE SURE TO PLAY WITH HER CLITORIS!!! the clitoris is the nerve ending at the top of the vagina that is hard and sorta pokes out. this is the most sensative spot of a girls vagina and they love when u mess with it. don't be shy and flip it around with your tongue, also suck on it if you feel the need. do not over use this part of the female body for overuse can cause her to feel numb there and not get any more pleasure for the duration of the night. 5 min intervals is a good time limit i think.
another good thing to do while eating a girl out is to put your lips around the clit and hum. this acts as a human vibrator and is sure to get her to scream or at least show that she is loving it :D.
Now you should be all set to give that special someone a great time.
RMEMBER!!! ask the girl before you attempt this or give BIG hints that your going to because some women do not like being eaten out because they believe it is nasty or they may not want u to do it at that time. so be sure to make sure they want it. Also its a good idea for them to take a shower before you perform this because they urinate from the same general area.