Marriage is a legal joining of two people - religion does not need to be involved.
A judge, justice of the peace, notary, or anyone else who is certified to perform marriage ceramonies can legally marry you. You must get a marriage license from your local court house and fill out the proper paperwork. Most states have a waiting period of 2-3 days after you recieve your marriage license before you can actually have the ceremony and get married.
You can have a wedding just as any religous person would. Find a venue (rental halls, outdoor wedding, town hall, etc) and have a ceremony. It is exactly the same with exhanging vows, just the religous aspect is not a part of it.
You can also just get your license and get married by a judge, notary, justice of the peace, etc and not have an actual wedding. Me and my husband were married by a Notary. It was just me, him, and the woman marrying us.
I think what "thespian" is trying to get at is that whole aspect of marriage that is primarily concerned with sacred vows before God and the church...
Atheists are people and while I do not know any atheists, I do know that they do have the right to marry and decide to believe in God or not...
As two atheists you can arrange to marry just like anyone else. The only requirement is the legal one and that varies from country to country. Other than that you can make whatever arrangements you like.
There's nothing wrong with atheists marrying, it's not like it's illegal for them to marry, people choose to get married on beaches, etc as well these days so I don't see how it would be a problem
It's not illegal, you could still marry someone without a priest. Personally, i think weddings are more meaningful when the couple says their own vows