I know this might seem a bit novel, but -- ask directly ;). Then the second part is to mentally prepare yourself to either answer, and try to detach from the outcome so you're not too nervous to ask in the first place. In other words, figure out ahead of time how you'll be okay regardless of how this person answers.
So without further ado -- the asking part itself. It does depend a lot on the individual person. I will admit that I'm kind of weird and out there, but I have yet to be turned down when I asked someone out. My invitation has ranged everywhere from a very blunt, "You smell nice. Want to go to the movies?" To, "Oh, you like ice skating? I used to figure skate, and the rink is open. Let's go, I'll pay for your rental." (apparently this directness is a little less weird in cities, but I'm a small-town girl and people are NOT used to it :P )
I have gotten some really weird looks in the past, but hey, I certainly stuck out in their minds. I think the biggest reason I haven't been turned down is because I'm upfront, matter-of-fact and relaxed about it. There's no nervousness or emotional charge -- I don't feel pressured, so neither do they. I didn't end up dating all of these guys, but I did end up with some awesome friendships that are still intact today. Asking out is about getting to know someone better, so the delivery is just the same as, "Hey, you're cool, let's go for a chat." After that, if you continue to be honest every step of the way, most other people will too. It's kind of scary sometimes, especially if you really don't want to creep them out, but it pays off and really tells you whether this other person is good to be around or not.