This is a great question and I'd love to hear from others who also do freelancing.
From personal experience, I would definitely suggest an hourly price for website creation or any project that may have lots of changes/updates. I remember when I first started doing web work on the side, most of my clients were friends or family. So I would try to give them a break by giving them a fixed price.
Bad idea. Of course if you allow people to take advantage of that they will. So that's exactly what would happen. People always underestimate how much time it's going to take to make changes, revisions, etc. And development (websites and even apps) is so subjective there are always going to be updates/changes that weren't necessarily in the scope.
I don't have a set price. It really depends on the work and how involved. But I will give them an hourly price (let's just say $100/hour). I will also estimate the amount of hours upfront so they have a ballpark idea. And if an updates will go beyond what I estimated we will address that.
I also collect the first 50% upfront -- especially if it's someone I just met (for example I meet a lot of people at various local WordPress meetups, etc.)
As far as getting jobs, you can try some of the online sites like freelancer, oDesk, etc. And you can look at existing jobs to get an idea for what people are charging for their work. A lot of the jobs are public. The nice thing about working for freelancer, Elance, etc. is both the buyer and the coder have some level of protection through the site.
You can also set your terms for how you want to be paid as well. So that's another bonus.