I did a lot of session work in the late 60's and through the 70's. In the 80's I lost a lot of work to drum machines - so I bought the various current machines and learned to program. Then electonic kits can out - so a session drummer needed to keep up (I bought Simmons, etc - right up to the Roland Vdrums).
I don't do a lot of session work any more - in part cause I'm old (newer younger players are more "in the loop" (which is how it should be) and in part cause most of the "real" studios have given way to home studios and things like Acid and other drum loops.
So - to be a studio drummer, be prepared to accept that it rarely provides the level of income it did many years ago.
1st - Understand every musical style - and do them all very authentic - have good tempo and know how to play to a click
2nd - Know how to read, although there are sessions that don't require monster reading skills you at least have to be able to read a basic chart.
3rd - Have very good gear - while some studios have kits, you will be required to bring gear more often than not
4th - Know how to tune your drums for quality tone in many styles (ie rock tuning, vs. jazz tuning, etc) - this often requires more than one kit
5th - Be a very nice person who is dependable and does not cause waves - and be prepared to work under stress and tension without getting upset
Naturally there's more - but that's a start.
How to break in?
1. Have a demo - play several grooves in various styles - no solo's - this is all about the groove
2. Hang around some studios - offer to be a gofer or do whatever you can to hang around and be helpful - maybe after so due paying, you'll get a chance - don't expect to get paid, for a while
3. Offer to play for free. Maybe you know some people with home studios who can use some free drum tracks
4. Gig out. The more musicians you work with - the more your name gets out there - a lot of my studio gigs came from going in the studio to do recordigs with bands I was in, and the engineer or producer asked for a card
5. Hang out at clubs and other music venues - meet people - network
6. Hang out at music stores - post cards, etc.
7. Network, network, network