Since I've never really asked anyone out before I don't really know how to do it. Also, are there any
special considerations for asking out someone at work?
So far as I can tell, formal "asking someone out" isn't really something that people do much anymore. More often, you meet people, get to know them, then after you already know they'll say yes you invite them to coffee/dinner/whatever.
Alternately, find some hobby and let it be known at the office that you enjoy it, and make a general policy of inviting and accepting
anyone who's interested in participating. When everybody knows that you, that guy from acquisitions, the IT manager and one of the sales staff all do movie night every Saturday, that completely eliminates all the stress and drama when you invite Miss Sexy Future Girlfriend from accounting. Or go paint balling. Or go miniature golfing. Or do SCA heavy weapons combat. Whatever. Could be something as simple as going drinking together. Or maybe you don't even do the same thing, but it's known that you have a regular get together
outside the office where you do fun things together.
That's the key. It's less stress for both you and Miss Sexy Future Girlfriend because it's not a date. But, after she's started going out with you every week (key words: going out with you) doing whatever innocent, fun, harmless low-stress low-drama thing that you all do together, then she's already used to the idea of (key words) going out with you.
Note that when you do this, I advise not getting too attached to any one particular specific Miss Sexy Future Girlfriend. Whatever you go do, make sure it's something that you'd enjoy doing anyway even if you never convince Miss Sexy to join you. That will eliminate a lot of the artificialness from your demeanor and you'll be more "the real you." Plus even if she never joins you, you get to have a good time anyway. And then end up meeting somebody else instead.
please, for the love of everything holy, unholy or whatever it is you love, refrain from dating in the workplace.
Why? For most people past their college years, work is the number one source for meeting people. Bar-hopping doesn't really work.