This depends on a few things:
1.) How soon do they need this website done? (If it's a rush job, you should charge more than if you can work at a comfortable pace.)
2.) Do you have qualifications that make you more valuable? (College degree, similar experience, etc.) If you have no experience or credentials you'll have to start out less expensive.
3.) How dense is this website? (Is there one small marketing paragraph per page or loads of highly technical copy?)
4.) How organized is the client? (In other words how much groundwork are you expected to do?) Do they know what they want and have information for you to draw from, or are you starting from scratch? The more research and thinking you have to do, the more expensive it should be.
5.) Are they are major corporation with a big budget, a friend or relative who wants to try going into business, or something in between? (Friends should get a discount, if you bid too inexpensively when it comes to large companies, they may think you're unprofessional.) Has the client discussed pay with you? They may have a set budget.
6.) Beyond money, what is the value of the project to you? Can you use it for your portfolio? Is it an interesting job that you will enjoy? There are other compensations besides money.
7.) Where do you live? Big city rates and small town rates may differ.
10.) Can you work for home and set your own hours, or do you have to show up on-site?
I would suggest that you find a rate between $20 and $40 per hour and stick with that.
If it's a small project, you could potentially give it a set rate of a few hundred dollars. HOWEVER - if you do this, then you must specify a limit on the number of rounds of revisions (changes and edits) that you will include - otherwise you may end up spending too much time for the money.
I would suggest that you get client feedback at certain points (after writing the outline, after writing the home page, etc. to ensure that you are on the right track and that they like what you're doing. This way you will have fewer revisions.)
If these are people you don't know - and a company that is not established, get a signed contract that gives you a down payment (retainer to work against) plus a payment midway through the project and a final payment upon delivery.