I agree with everything Tex said. I'm a drummer who has freelanced with different bands and in different studios for years. Although I now consider myself "semi-pro" - I was a full time musician for several years.
It is all about networking. But you have to have chops (in almost every musical style), and you must very very dependable. Your gear must be in flawless condition and you must be able to at the drop of a dime reproduce any tone from country chickn' pickn' to warm jazz tones to screaming distortion. It is essential that you are easy to get along with and that you can take constructive (and sometimes brutally honest criticism). The ability to read well may not always be required but will on occasion be required.
You need to be able to produce in demanding and sometimes stressful conditions (if you're being paid to find your tone and hit your part - you need to do it in the first few takes). You need to understand obscure directions (I need it heavier, or lighter or cooler or funkier, etc - when none off those terms mean what you think they mean).
The best way to get into studios is to know producers or engineers who will recommend you. The next best way is to gig with hundreds of different musicians who can recommend you (assuming those musicains had the chops to get into the studio scene to start with). That is how I got my in - playing with everyone I could eventually got me into studios which gave me a chance to meet produceres and engineers.
If you can't get in that way - as Tex said get a demo of your chops (in several styles), get business cards and start knockin on doors. If they let you, hang around studios as much as you can and be willing to work for free or to do whatever your ethics will allow to get your foot in the door.
Real studio work (jingles, film work and label artist projects can be hard and demanding work - but can be both financially and more important, musically rewarding.
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