Well... where does one begin. Going down on a woman is different each time. I mean, each woman is unique in what she likes. There is a general road map that one can follow that works in most cases. Rarely have I seen it fail. There are two ways to go down on a woman. One is to go straight for the kill and try and make her orgasm as fast as possible. The other is the foreplay version. I'll explain the foreplay version as it is just an expanded version of going for the kill.
Having a dextrous tongue helps in any case. However, for those of lesser lingual abilities, here's a run-down. Start by licking around the pussy. Keep the tip of your tongue within a one inch radius of the pussy lips. Doing this will get her aroused and cause her juices to flow. When she's wet enough, you can insert one finger into her pussy a little bit at a time until it's knuckle deep. Slowly start to push your finger in and out. When your finger is wet, take it out and rub her clit in circles. Not too rough and not too light. Always make sure that if you're rubbing her clit with anything but your tongue, that it's properly lubricated. If it's too dry it could be uncomfortable for her.
Now, when you can tell that she's becoming very aroused push your finger back into her pussy and then start to lick her clit with your tongue. Try and make your tongue as firm as possible and to a point. That way it will be like a wet finger rubbing on her clit. With the finger in her pussy insert it all the way and press against the outside of her pussy with your fist. Curl the finger inside of her upward, toward her belly button. Now, the variation of how you move your tonge differs. Some say make the alphabet and numbers. I find that any random movement of the tongue in an up and down motion causes the same effect.
If you continue to vary between licking her clit and rubbing it with your finger you can keep her on the edge. If you keep using your finger and tongue, it will eventually push her to climax.
Everyone has their own style.
Another thing that helps is lightly pinching a girls nipples. Just the nubs. These are a direct stimulant to her clit and will help her to come faster.
Hope this helps.