Session time depends on many, many factors. I normally get about $100 per session, (assuming about 2 hours) although I have worked for less and for more. There are people who can demand double or triple rate (because they can make it happen).
If you are in a large market, with a lot of competition, you may have to work for less (although there also may be more opportunities). If you are new, with no network (contacts), you may have to work for less.
If you are hired by a producer, with a budget financed by a label you may get more. If you are working for an independant or directly with a singer/song writer (with no label backing), etc you may get less (many people do sessions for free to get experiance and to make contacts)
Session work is very demanding. You are on the clock and you are expected to produce the goods (whatever that may be) qucikly with limited delays and no bullshit. If you can produce the goods, word may get out quickly. However, if you can't produce the goods, word gets out even faster. Once you blow it the producer, engineer and anyone else on the session will likely cross you off the list.
You need excellant gear and you need to know how to use it - to get whatever sound/feel the producer wants instantly (often the producer doesn't really know what they want - but they know it when they hear it). You need to take direction without getting an attitude and you need to be profession and easy to work with. This is the session player's primary purpose in life - make the session go smooth, for the producer, the engineer and the talent.
It can take a long time to go from "new guy at the session" to the A list, but being crossed off the list just takes one bad session.