A VA approved lender can use an online program called ACE--the Automated Certificate of Eligibility--to get you started in the VA loan guaranty process. Unfortunately, the automated system won't work for everyone. Some people don't have enough information in the ACE database, and are required to fill out a VA Form 22-1880, a Request for Certificate of Eligibility. If this applies to you, simply fill out the form and mail it to your regional Eligibility Center along with supporting paperwork including a copy of the DD-214 discharge paperwork.
Don't send originals of the DD214, a photocopy will do. The certificate of eligibility process can be tricky for veterans who were separated from the military with a discharge other than honorable. In this case the VA must investigate the discharge to insure it was not classified as dishonorable. People who fall into this category should seek help from their local VA office, especially if you need to file an appeal to the results of your request of eligibility.