A large amount of studio business comes from word of mouth.
Obviously, to get the word of mouth moving you need some initial clients that you can hopefully impress (or at least satisfy).
At first you have to be an aggressive salesperson, with a quality product at a very fair price (until word starts to spread).
Some possible places to get clients would be:
1) Open mic nights (open jams) where you may find singer/songwriters or other musicians who may want to record their songs/playing
2) Nightclubs and other performance venues (in particular that present original music)
3) Churches/schools that have music programs
4) Talent agents/management company (that may need demo's)
If you have writing, producing and arrangement chops you could also try to solicit jingle business through local marketing agencies, radio stations and businesses. However, this is a very competitive field with extremely talented people trying to get the same business.
It helps to have a demo recording of a few songs (in particular in the musical styles you are trying to book into the studio). Hopefully, you have the chops and the sound quality to prepare a good demo. It also helps to have a rate sheet (how much will this cost?) and a list of the gear that you have. A picture of the studio is always good eye candy.
If your studio is not stocked with the greatest newest gear, then you need to "sell" why your studio is the best choice (fair rates, relaxed setting, best drugs in town - just kidding!!!).
Always, always, conduct yourself as a business professional (this is business right???). I find even with "burn out musicians" when I conduct myself as a professional, they seem to try just a little harder to keep their act together (at least when they deal with me).
Naturally, the risk of this cold call marketing is that you are informing total strangers that you have valueable gear at your facility - but that is a risk you may have to take. Hopefully, you have a secure facility!!