How do I determine how much to charge for advertising on my website?

Do some competitive analysis and see what sites like yours charge on their sites. If you know people in media buying agencies, they might be helpful but in general advertisers pay for audiences in terms of CPM/costs per thousands of people viewing the ads or CPC (cost per click), etc.

Unless you want to be managing this process it might be more efficient for you to find someone who can do this for you on an outsourced basis.