Listen! The most basic advice to get and the absolutely hardest thing to do ;) If the subject is too awkward you'll notice if you really pay attention to her. She'll for example maybe look away from you, and hesitate before she answers, or just stay silent waiting for you to drop it.
Also when you say something stupid, acknowledge it instead of trying to hide it! Make it into something funny or self ridiculing instead of awkward and switch subject, most girls will appreciate both the humour and the getting-rid-of-weird-situation. Dispell the awkwardness by saying, "oh man, that was stupid now I'm switching subjects. Do you like cheese?" (extra points if she knows the movie the cheese reference is from ^^ If you wanna ditch the it just substitize cheese for ice cream or something), or "That was really out of orbit, I need to get back to earth now." Or you could say "I'm just noticing this is really awkward, don't you think?" Takes away a lot of tension just to mention that it's there.
Just noticed I'm on a whole different page from dsc2222 ^^ But we both have sound advice, just check for what applies the best to your situation :)