What is the best way to 'finger' a woman?
Gently, especially at first. Be sure you have clean hands and that your fingernails are not long or rough. Avoid touching her with your nails. Be sure there is plenty of lubricant, either natural, which is caused by her heightened arousal from your other foreplay, or there are products that can be used (some of which provide a heat sensation to add to the pleasure).
Don't ignore other parts of her body, use your other hand or lips (or other creative body part) to caress and touch her breasts, lips, ear lobes and skin all over her body. Touch all areas of her genitals first, don't just go straight for the clitoris. Ask her what she likes, talk to her as you do things and ask her how it feels. Talking about it is very stimulating to some women, but others may not like the conversation, you'll have to explore and find out what her desires are.
Caress, stroke, and rub...don't poke. Glide your finger (or two or even three fingers if she is not too small) rhythmically in and out of her vaginal opening, but teasing a little by moving away from there and touching the outer labia and inner thighs briefly before you go back to the clitoral area can excite her more. As you penetrate, gently touch and rub the clitoris.
Ask her to guide you with her hands to the places that feel best, she may even enjoy showing you the places by touching them (seeing and feeling this may be very exciting for you, too). Once you bring her closer and closer to orgasm, the strokes should be faster and targeted at her favorite places to have you touch.
There is a place about two inches inside her vagina that is called the "G Spot". If you can find where that is in her body, gentle stimulation there as well as across the clitoris on your way to it, can bring a more intense orgasm than one brought on by clitoral stimulation only. It is on the front wall of the vagina and is about quarter sized. Finding it can be a joint project if she isn't able to direct you immediately to it (ask her), and the experimentation and "game" finding it can be very rewarding for both of you.