Fingering is the grand art of masturbating your woman's vagina with your own fingers. It involves much more than just sticking them inside her and moving them around. The most important thing you can have when going into something new is knowledge. It's also very, very important to have a partner who can talk to you about this and give you instruction during the act and afterwards. This way, you can both learn more about each other's intimate perks, secrets, and desires. You'll also find that if you make her happy, you'll be happier as well. It should be noted that the guide that follows is one example of guidelines. These specific techniques aren't necessarily going to work for all women. You'll honestly need to consult with your partner on what works and what doesn't, but these will be some starting tips. Just remember to keep the communication channels open, and don't be afraid to add a little variety.
First, when rubbing her clit, up-and-down motions usually work better than side-to-side or circular. Sure, you can use the latter two to vary it every now and then, but, on the whole (whether fingering or using your tongue), up and down on the clitoris usually works best.
When actually using a finger or two inside of her (I'd suggest one for tighter girls--you CAN fit two, usually, but you lose a lot of maneuverability, and she'll be sore afterward), one of the better motions I've found is to push your finger all the way in, then bend it slightly when pulling it out, so it scrapes against the top of her insides. Not only does this feel really good, but it gives you a chance at hitting the G-spot. If you do hit it, you should be able to tell by your partner's reaction. And, trust me, you need to find the G-spot sooner or later (sooner the better), and use it to your full advantage. That's one of the best places to start consistently rubbing when she's getting close to orgasm.
That's another thing- try to be consistent. You can vary your angle and fingering style sometimes during the session, but don't change every three seconds. And when she gets close to orgasm, DON'T change unless she tells you to. Get a little rougher and pump your finger a little further into her, great. Go faster, wonderful. But DON'T decide "Hey, maybe if I completely change my angle and rotate my finger THIS way" when she's near the edge- every time you switch, it sort of knocks her orgasm back a bit, and that can be really frustrating for her. And most importantly, when she's getting closer to orgasm, if she says for you to do something, DO IT. Harder, faster, rougher, whatever- she knows what she needs, and it'll help her orgasm along a lot if you just listen to her and do what she says. This is for HER, after all.
Also, pay attention to more than her genital area. I know it takes a lot of concentration to finger a girl, especially when you're new at it, and so you sort of forget to do anything else, but it makes the girl feel better and increases her general body sensitivity if you nip at her thighs, rub her stomach or breast with your free hand, do SOMETHING. Mostly, it helps her feel like something more than just genitals to you, and that means a lot to her general pleasure. You may even want to stop every now and then (provided she isn't close to orgasm because that would be just mean) to just hug and kiss her for a minute or two. It would give you both a break and would preserve the intimacy of it all.
You can get a lot of pointers if you ask her to touch herself while you watch, and then pattern your motions after her. In fact, the first few times, you may want to ask her to finger herself or rub her clitoris herself, so that you can take care of just one of those aspects and learn what feels good while watching what she does on herself that feels good in the other area.
Talk to her during the act. Tell her that she's pretty, ask her if what you're doing feels good, tell her you want her and that you like doing this, that sort of thing. That helps keep the intimacy going, making her feel like a person and not just a vagina, and also reassures her that you aren't bored. Many women are sort of paranoid that the guy isn't having any fun at all- make sure she knows that you are. Even after you are done, fully clothed, and alone, make sure to remind her just how much you enjoyed doing that for her.
Especially right after she has reached orgasm, don't pull your finger out suddenly. Unless it's part of hard, fast thrusts (and usually even then), your finger should stay in or come out very gradually. Ripping it out all at once can be very uncomfortable or painful for a girl. Sliding it very slowly can even serve to tease, and make sure you look her in the eyes and grin when you do this. She should love it.