A ceremony is legally required in order to get married in the USA. You can't just sign paperwork and walk out the door.
However, a big white gown is not required. A church ceremony is not required. Rings and a kiss are not required. Guests are not required (although a witness or two might be legally required; however, some places may provide you with someone, if you do not want to invite anyone you know to be a witness). A big party after your wedding is not required.
You can ask the courthouse/City Hall if they can perform marriages there. If so, that's one option for you.
If you're religious, then contact your minister and ask what your options are. You could marry in your house of worship even with no guests, or in some religions the minister will come to your home or another location of your choice and perform a ceremony for you.
You could hire a professional wedding officiant to come to your location of choice and perform a ceremony for you - your home, a public park, a B&B or hotel suite, whatever.
If you're inviting guests, then you need to arrange to have chairs for them during the ceremony, and you'll need to feed them afterward. At a minimum, serve a grocery store cake and some coffee or punch. Or you can take them out for lunch at a restaurant, or even a casual place like a burger joint or pizzeria. Or go back to your home and serve some homemade food, or a little cake, or call and order takeout.
If you're not inviting any guests, then you can do whatever you want once the ceremony is over. Go on a trip/honeymoon, go out to eat, go back home and canoodle, go back to work for the day, whatever you want.