Step1
There is a girl you want to ask out? First prepare yourself mentally by understanding that your chances of getting a no when you do ask out this girl, are much higher than getting a yes (the best of the best of the best in the world only get a yes 20% of the time from strangers, and about 60% from women in social circles), and there is nothing you can learn on eHow or anywhere else that is going to change this. Go in expecting the best when you ask out a girl, but prepared for the worst (this is what we call acceptance confidence, being fine with "luck" and going after it anyway).
Step2
Once you are mentally prepared, and determined to have fun no matter what happens... Realize that you need to detach from "wanting" something out of this girl when you do ask her out. Have the attitude that if she says yes, that's cool, if she says no, that's cool too. (This will increase the odds of a yes tremendously as well). Your only goal is to have a fun, interesting conversation, not to ask out a girl.
Step3
Talk to the girl, laugh, have fun, and tease and joke around (if you can't do this, than look at the resources at the very bottom of the page). There's two ways to take it from here:
1) When you're both in a great mood, at the peak of laughing and joking around, just go "hey let's go here", and take her to the cafe nearby, a park bench, a stroll on a path... Guess what, you've just *asked her out*! This is called an "instant date". It's much more romantic, spontaneous and preferable to a formal "date request" where you verbally ask a girl out.
Sometimes a formal request is needed though, if you happen to always be in a situation that doesn't allow an instant-date. In that case...
2) When you are both at the peak of a fun, enthralling conversation, just say "hey, i got to go do (whatever it is you need to do), let's continue this conversation over a cafe at so and so this Friday". At this point she will either:
a) Say something like "sure, i can make it there by this time", or "sure, i can do that", "yeah, let's do that"... this is a yes.
or
b) "oh, there's plenty of time friend", or "maybe some other time" (without offering that "other time"), or "oh wow, my cat died, i am burying it exactly on Friday at that time"... answers like these are no. Basically any "excuse" where she doesn't offer an alternative is a no to you asking her out.
Now you know how to never get stuck with one of those... how to ask out a girl questions, which might make you raise new questions such as "how do I overcome my fear from doing it or the fear of rejection. Look into the the different resources at the bottom of the page for those specific questions.