Neo, my first few 'date' experiences were downright terrifying. But I will tell you that the anticipation of the event is the absolute WORST part, and it does worse by us than the actual date does.
First off, coffee is a great date idea. It's neutral, it's brief, but allows conversation...and on that rare instance you guys REALLY hit it off, you can always say "Hey, let's go for a walk".
My first advice to you, as someone who has struggled with anxiety and awkwardness and repeated the 'first date' experience a number of times, is to find some way to relax before the event. Exercise, stretch, breathing routines, Yoga...find SOMETHING (besides substances) to calm your nerves.
Make sure you are dressed properly for your persona and the occasion. Look good, but be at ease and be neutral. No shirts with words on them, no pants with chains hanging off the butt (save that for when you guys go to a rock concert). Make sure you have a fresh haircut, fresh shower, and at least deodorant. Some sort of smell-good won't hurt you, either.
The hardest part will be talking to her. This is usually attributable to the fact that women are creatures of unadulterated, universal EVIL and SNEAKY MALCONTENT planning to destroy you in one way or another, disguised to fool your instincts in to thinking they are pretty and nice smelling and enjoyable company, and it is normal to be uncomfortable when speaking to such wicked constructs of life and limb. Anyway, there are two basic ways of making conversation and getting to know someone: Sharing, and Asking. Do a little of both, but do more Asking. If you're going to share, try and have a good story or two about yourself. If you can make her laugh, and laugh with her, that's perfect; so don't worry too much about sharing 'embarassing' things that aren't too personal.
Good things to ask are questions that are either open ended, or require her to tell a story of her own. Generate further questions from what she tells you.
So far I like to go with asking what a girl's goals are; but don't be mechanical. In other words, it shouldn't sound like she's filling out a resume or questionairre. Instead of 'What are your goals?', ask "So are you in college?/Do you want to go to college?", or if she's told you her job, playfully ask "So what do you WISH you were doing?" Or ask about her family. If you need to break some ice starting off, ask how her day has been. If she's clammed up at first, talk about yours then ask about hers. Ask her if she's travelled, or where she would go if she could. This is a good time to then Share your equivalent thoughts. I used this as a talking point with my girlfriend when we first went out and ended up learning that she'd been to a number of interesting places; then I showed off my knowledge of Norse history/ancient religion, which caught her interest. Make sure you are attentive to her, but ALSO make sure to paint a picture of your qualities! Unadulterated Evil does not like boring, and you are NOT boring, you just haven't shared what makes you interesting yet (or perhaps you haven't developed it fully).
Ask her questions that will make her think. Make her tell a story. Start with what you know about her and go from there. If all else fails, ask something TOTALLY out of the blue to make her laugh. One time I asked a girl what her plans were for the coming apocalypse. It continued the conversation for ten minutes.
Your body language will be very important. Try to relax. Don't tighten your shoulders. I like to hold my coffee with one hand and drape the other across the back of my seat so I can't do anything dumb with it.
Above all else, accept that as an adult experiencing a first date, there is a high probability that this will absolutely not work. This is practice. And you WILL get better at these things by putting yourself in regular exposure situations to gain practice.
Good luck, and let us know what happens.
! 
