Google Adsense:Clearly one of the most popular means of generating revenue with your existing website it to sign up for a service like Google Adsense, whereby you add additional code to your website that facilitates the placement of contextual ads within your site, in hopes that your visitors will click on them. How much money you stand to make depends on how much traffic your site generates and how many of your visitors do actually click on any given ad.
Banner Advertising:Banners are essentially clickable graphics that you place on your website that advertise and link to another site, which then generally pays you for each visitor that clicks the banner. Conversely, some agreements are contingent upon the person not only clicking the banner, but then also making a purchase on the target website which could then potentially earn you a commission for that sale.
Affiliate Programs:Essentially what affiliate programs do is to pay you to refer people to them. As an apt example, HostGator has a rather successful affiliate program whereby we pay you to refer Customers to us: http://www.hostgator.com/affiliates.shtml ...you simply place a link on your website that someone then clicks on to sign up with HostGator, and we then pay you.
Donations:If you feel the quality of your website is worthy of people simply handing you money, then by all means you may certainly ask for donations. Paypal makes it incredibly easy for people to give you money with the simple click of a mouse.
***There are numerous other means of generating revenue online, some more respected than others. For example, you could run pop-up/pop-under ads, but those are generally considered a more of a nuisance than anything else. You can offer memberships to premium content, if that is applicable. Offering something for sale is always an option; perhaps even an ebook on how to monetize websites.