Okay, what if you start the conversation out by admitting just that? Say, "I'm terrible at this. You might have to cut me some slack until I get to know you better. I'm not always this awkward." Would that take some of the pressure off?

Or... what about asking someone out to the movies? You're not supposed to talk during a movie (wish everyone understood this). That would give you some time to sit next to her and get yourself settled down before conversation was required.

Where is this coming from, anyway? Are you just terribly shy? Anyway, practice makes perfect. Start conversing with strangers, like the girl at the video store or whatever. Two sentences. "How are you today? Thank you very much." carries very little risk, and therefore should not make you too anxious.