I've had some good results with
http://peopleperhour.com/ It's a bit smaller than a Elance, Freelancer, etc. Really though, all these 'standard' freelancing sites are the same.
Some tips I'd probably give: focus on listings in your own country/area, you will have better results. Don't be too formal, try to build a good rapport while staying professional (especially in proposals). Focus on things that you find exciting, or you'll get bogged down.
No idea what your background is, but web dev is the best area to be looking in. PHP et. al. have thousands of available at any time, at a variety of difficulty. Finding clients that will let you work in more 'trendy' (i.e. fun and productive) languages is a little harder, but if you're really pedantic you can find them.
Pay rate is very variable. One thing I've noticed is that a lot of clients just don't know what they should be paying. Most sites require an 'expected budget' on listings, but you can usually budge this up quite a bit if it's too low. Keep in mind if you're in the UK, EU, etc. that you're competing against developers in other countries with lower living costs, and that a lot of clients (especially on simpler projects) don't always have the budget you might be looking for.
The most important part of freelancing isn't your tools or your programming skills or how much time you have available - it's how you communicate with clients, especially non-technical ones (i.e. most of them). Email regularly. If you're in the same city and the project will take more than a couple of weeks, meet up for an hour to introduce yourself and discuss requirements. Always explain what you're going to do, and if you have any doubts at all, ask about it. A misunderstanding is easily made when working remotely.
I'd recommend you go into it (for the first few jobs) without worrying too much about money. Take projects that look interesting and at least cover your costs, and get a feel for how the process works and how you can attract better clients.