Even if it's intended platonically, asking a girl to spend time together can be intimidating. When you don't know what her reaction might be, such a simple proposition can seem nearly impossible, so it often takes some mental preparation to request the pleasure of a girl's company.
Make plans before you ask. Be sure to have something in mind when asking for her time. It can alleviate pressure for both of you if you already have plans with friends and you invite her to come along. Public places, like bowling alleys and the beach, are the best ideas, especially if it will be your first time hanging out.
Be confident. You believe that she is an interesting person to hang out with, but don't forget that you are, too. Most people are drawn to confidence, so try to avoid sounding desperate (“Would you please come with me...?” or “Maybe we could go there if you want to and you're not busy...?”). Don't come across as demanding, but remind yourself that your company is valuable, just as hers is.
Make your intentions come across as light and friendly. Even if you have hopes of dating this girl in the future, asking for a date right away can be nerve-racking, especially for her. It's also a good idea to hang out as friends before trying for a relationship right away. Keep things on a friendly level, and she is bound to respond more positively.
Don't feel rejected if she turns you down. If she says she's busy on the day you suggest hanging out, offer to get together some other time, and exchange contact information. If you invite her to a skating rink and she says she can't skate, it doesn't necessarily mean she doesn't want to do something else. Pay attention to her body language to know when to suggest other ideas or when to give up.