So you have found a girl who is so wonderful you want to have her as a girlfriend. Congratulations! Now comes the scary part, asking her if she feels the same. There are a number of ways to do this, a lot of which depends on your personality and the kind of relationship you already have with her. Here are some tips on how to first make sure she feels the same way, and then how to ask her in a way that makes her feel special.
First: Get to Know Her
This step is already complete for many people. However, if you like her from afar, and aren't friends, casually dating or hooking up already, then you need to start with a date before jumping straight to girlfriend. If you really like her, the best way to do this is to be straight, and not play angles. Don't arrange to show up where she is, but just go up and ask her if she'd like to do something with her. You will get bonus points if you choose an activity she loves over making her go somewhere that you like but she doesn't.
Second: Make Your Intentions Clear First
Asking her to be your girlfriend shouldn't come as a surprise to her. If you're into her, let her know you're into her. If you're shy, you don't have to say it directly, but you do need to make sure you listen to her, show her you care about her needs, and bring up conversation topics that are important to her like her family, friends, job and hobbies. Spend time with her, but don't crowd or stalk her. Make yourself available when she needs you. Once you have established a clear emotional connection with her, the transition to girlfriend will be easy.
Third: Ask the Question
This is the scary part. However, if you have laid the groundwork and you have gotten positive signals from her, then it shouldn't be too bad. If you are getting mixed signals from her, or she is not very responsive to your intention, then you may want to either wait or look elsewhere. How you do this should depend on both her personality and yours. If you want to do something big and showy, make sure both of you like being the center of attention before you do that. Then, check out flash mobs and other public proposals, and create a scaled down version. If you want to do something special and private, then the biggest thing to consider is what she will think of as romantic. Weekend camping, five star restaurants, or a weekend beach resort getaway all appeal to different kinds of girls (though some like all three), so show her how well you know her and make her feel special.