How do you ask a girl out without being embarrassed?

You never know if you will get rejected or not, so you have to take the risk. The best way might be to either write it down in a note or make a phone call.

No one likes rejection, but everyone faces rejection during their lives. It is how we deal with it that matters and it should be taken "with a grain of salt." The worst someone can say is no and so what? Just move on.