The most important thing for those new to working in a freelance or self employed capacity is to realize what it is that they are pricing. 

Whatever fees you change will have to take account not just of the time you spend on the site but on the fact that you will have overheads. These may include, even for someone working from a computer in their bedroom, hosting for your own site, paying for your Internet connection, time and money spent on marketing, the cost of software, hardware and business materials, of any professional advice you need from accountants or attorneys, of research, continuing training to expand your skills and keep them up to date, telephone and power charges and so on.

It is common for new designers to under charge for their work, partly because they underestimate what is involved in a project but also because they lack the confidence to ask for more. There are many other reasons why you might legitimately charge less for a project than even you know it is worth; perhaps it is one that you know will fill a gap in your portfolio, is high profile and will therefore result in valuable exposure or will allow you to put into practice or learn new skills. 

It is also quite natural that your first few sites will be cheaper for the client than if they had chosen a more experienced designer, and that is as it should be. But you still need to charge a fee you are comfortable with and that does not make you feel hard done by. You need to be clear that the price you are charging is one you have fixed on as sufficient for you, given the circumstances, rather than one you have been pressured into by the client. Even at this early stage if you start to feel you are being taken advantage of, back off and consider careful whether or not the benefit to you of taking the project outweighs the financial implications. If if does not, do not be afraid to say no.

Later on you will be able to increase your prices inline with your experience. When and by how much? The best guide to that is how well you are doing. If you are busy and finding it hard to get work finished, then increase your prices - it is far better to have two high paying projects on the go than a half dozen poorly paying ones.