It's a difficult problem we all seem to get in; you start feeling for your best friend, or girls close to you who you get along with so well. The problem is, what if they don't like you back? Fear no longer, for there is a way to determine if she likes you, figure out a way to ask her out if she does like you, and hopefully live happily ever after.
As a start the most important element is to ensure that this girl really IS interested in you in return. This is unfortunately the part where even I myself go wrong, in that you assume because she is fun, flirty and loves to talk to you, that she has an interest in possible dating. The problem is sometimes girls are just like this with every guy, even when they are already happy in a relationship. This is generally because they merely love the attention and thrill of flirting with another guy, even if it will never lead anywhere. Not that girls in relationships are always happy, she may be on the lookout for a better guy, and luckily there is an incredibly simple way to check: Take a look at how she treats other guys. See how she treats her other guy friends, those in your workplace/school and so on. If she doesn't treat you any different she probably doesn't have an interest in dating you. That's not to say she'll never have an interest in you, just that you shouldn't make any moves yet.
There are many different situations you may find yourself in, as there are many different types of girls and many different levels you know each other at. So I've decided to figure out a generic system which you can use to figure out how to approach in the best possible manner. This is simply coming from my experience with many different girls and unfortunately every situation is different, so take it as a rough guide but don't live by it, use common sense too J, I'm really just generalizing here so find what best fits your situation and go from there.
There are 3 main categories for a girls social/outgoing level and because of this each type of girl should be treated with a different tact. While outgoing girls might like to go out drinking with you and friends, the shy girls may want something where they don't need to interact with others so much.
The shy quiet girls are girls who may only have other female friends and are almost never the center of attention, often spending a night at home or with their girl friends rather than going out drinking. One of the most common situations you will find yourself in with a girl is this one. Quite often it's that cute girl who looks like she could be really sweet and nice, but you just haven't gotten to know her, instead simply being an admirer from afar. The problem with this situation is that it's really hard for it to go anywhere especially if you yourself are very shy. Although there are pluses, generally shy girls will still go out with you even if they don't particularly like you (this is a good thing, for when you are out together you can bond and perhaps take it further) and usually if you break up afterwards it's easy to go back to how you were before. Most of the ways of asking her out can feel a bit awkward because shy girls don't give as much feedback and/or enthusiasm as others, ignore this feeling for its only going to hold you back.
One last thing that many guys fail to realize is that just because shy girls don't talk much or seem so excitable, doesn't mean they want something low energy like a stroll along the beach as a first date. Going out to a theme park works very well too, so long as they don't need to meet random strangers to have fun (ie. Pubs/clubs are generally a bad idea).
The Normal Girls are the middle of the road girls that are open and talk to everyone, girls and guys alike but won't usually be the kind of girl all the guys' desire. Normal girls are some of the most fun girls in the world once you get to know them, like the outgoing girls they generally have a very vivid, strong personality, but like shy girls they do tend to hide it from those they don't know too well. The thing about this type of girl is that her attraction level to you can greatly vary, and it often has a lot to do with how much interest she gets from the other guys. Unlike shy girls and Outgoing girls, normal girls should be done more on a case per case basis rather than just using a general rule on how to approach and deal with the situation.
For a first date, pretty much anything goes. Clubs may be a bit overwhelming unless they love going out and just dancing, but on the whole generally they are up for anything fun.
The Outgoing girls are generally either hot and as such get a lot of attention, or they are simply the fun, hyperactive girls who love life, being very flirty and out there. Loud Outgoing girls can be by far the most fun however they are also the ones most guys generally get confused by. The reason for this confusion is simply that outgoing fun girls are generally the kind of girls that love to party and are perfectly fine flirting with any guy just for fun (even if they have no interest in dating him). This is why it's best for any outgoing girl you ensure she treats you differently to other guys, she may be a lot more flirty than the shy girl in the office but that doesn't mean she likes you more than her.
For a first date the outgoing kind of girl generally likes something with a bit of social interaction, clubbing works well, as does just a general house party of your friends. The Outgoing girls are generally more high energy and like more excitement than most and as such a dinner date doesn't go down too well (it's sweet and all, but you will probably find yourself in the *friends zone* with her unless you combine dinner with something else exciting.)
One thing to keep in mind is that because Outgoing girls are by their nature, very outgoing, she will most likely chat to random strangers when out and about (clubs/parties and so on), getting jealous of it will only be detrimental, so you need to be able to let her go and socialize by herself without needing to be the only one talking to her all night long.