It’s a long process. It took us 3-4 years before we met all the requirements and was awarded a GSA contract. First thing though, you need an established business, with regular clients. Once you have that, you essentially leverage that experience and history to either bid on sub-contracts of the primary contracts that prime contractors have been awarded, and/or you start at the local government level, work up to state, then file directly for GSA status.
If you go to SAM.gov you can view contract opportunities, and they usually list out the requirements for each, where you can get a feel for what they’re looking for. Once you’re ready, this is also where you’ll register for account to bid, but I believe you’ll need 3 years of business history before you can do that. You’ll also need to register your business with Dunn & Bradstreet. If you already have an established business, or once you have a direction, let me know if you have any questions.