Easiest way is online, though you can mail your stuff in or call the VA and they'll walk you through it. Anyway, go to ebenefits.va.gov and log in. Once you've gotten through the security screens and notices, click "apply" on the left kinda near the top, scroll down to "housing" and to the right of that you should see something about a "certificate of eligibility". Click that and it'll walk you through the rest (it's very simple). Your COE is all the bank needs to start a VA loan process. To get the COE, you'll need your DD214 if you're already out, or some other stuff that's easy to get if you're still active.
A word for way in the future: If you sell a house that you've gotten with a VA loan, you'll probably need to reset your allowance on your COE to use it again. It's easy, but you have to remember to do it before you try to get a loan again.
Also, the first time use your COE, the VA funding fee is super low and independent of your down payment amount. Any future loans with your COE have funding fees that vary with down payment amount. However, on this same subject, if you have a disability of 10% (don't quote me on that number, I didn't look it up and I don't quite remember) or more, the VA funding fee is $0 forever and your down payment amount will never matter. Yay free loans! Now don't forget to go talk to the VA when you leave active duty to set up your disability. Even 0% yields some small perks.