Well it depends on the occasion. If it's for some event like prom, then you can make it public. If it's just asking her out because you like her, then you should probably make that a bit more private.
So if you're going to ask a girl in public, you have to be aware if she would like that sort of thing. Does she like getting attention or would she dread that a lot? If she likes it or at least wouldn't mind it, then go for it. If she's really introverted, I suggest to not even do this at all. So assuming that she would be okay with this, then here are some ideas that I've heard of that worked. Let's say that you have a class with her. You can get your teacher in on this and ask him or her to put up a PowerPoint presentation that day and have one or two of the slides be words asking her out in front of the entire class. Then you can come out and bring her flowers or something like that. So you see, this girl has to be okay with being in the spotlight and it should be for some sort of event like prom. But it's kind of cute and girls usually appreciate that kind of thing. Another one is to put on a flash mob for her. Yes, it's cheesy but it's cute too. And of course, the most cliche one is to serenade to her. Although it is cliche, it is still creative because people don't actually do that in real life. Well some do, but most people don't.
If you're not into being all public or if she isn't, then ask her privately. I only know of one way you can ask her out creatively though since usually, asking someone out privately isn't really cute or well known or both. Well here's one way that actually happened to me. So you know how most graphing calculators these days can type out words? Well you can write out a message in there, asking her out. Then go up to her and ask her for some help on a math problem or something and have her use your calculator. She'll read the message and she'll know that you're asking her out.
So there were a few ideas. I hoped they helped or gave you some ideas of your own. Good luck!