Study your craft. Attend a music school if you can afford it—demonstrated knowledge and ability, not a degree, will get you the jobs. This means learning the skills a studio musician needs, in whatever way you learn best. These skills include the ability to sight-read music, compose, improvise and play a variety of instruments.
Visit recording studios and talk to the producers and engineers. Leave a demo CD that showcases your proficiency on a variety of musical instruments. Include several different musical styles to showcase your diversity. As a studio musician, you can be called upon to play everything from country to rock. Ask to be placed on the studio call list.
Play in public as often as you can. Build a name for yourself and keep your skills sharp by playing with local bands, filling in for musicians when needed and networking on the music scene.
Build a portfolio and keep it updated with every new gig (job) you play, whether it's a live performance or a studio recording job.
Consider moving to the closest major city to you, or even going to New York, Los Angeles, Nashville or another major music city. Making a move such as this can be a big deal, but realistically, you want to go where the jobs are. If there isn't a studio where you live, your chance of getting work drops.