Summarize:

If you feel like you're not the most attractive, you may not have the confidence to ask a girl out directly. In that case, you can go about it in a more roundabout way, such as making an indirect suggestion that she go out with you. For example, you can ask her what she's doing over the weekend. When she responds, you can say, "That sounds fun. I'm going to see this new art exhibit that's supposed to be really cool. Maybe you'd like to see it, too?" One way to make it seem like you're not asking is to first ask for a recommendation of a restaurant or some other fun thing in the area. Once she responds, you can suggest that you go together, which makes it seem like her idea. For example, you could say, "Do you know this area well? I don't get over here much. Know any good Mexican restaurants over here?" When she responds with a name, say, "Oh, that sounds good. Want to show me the ropes there?" You can also try the opposite approach, where you talk about a fun or great place in the area. She may respond that it sounds interesting, and then you can suggest that you try it out together. You might say, "I've heard that place across the street has the best burgers." If she says, "Really? I love a good burger." You could say, "Want to try it out with me?" Another option is to just be direct. You may think you need to hide behind flirtatious questions, but really, most women appreciate when you're at least somewhat direct with what you want. Therefore, it never hurts to just ask, as the worst she can say is "no." For instance, if you've been talking for awhile, you could say, "You know, you're fun to talk to. How would you like to continue this conversation over dinner?"
Make a suggestion. Make it seem like her idea. Try your own suggestion. Just be yourself.