Frederik
My site is paid for by sponsors... er.. advertisers, but even before we started the sponsorship program people on the most part understood that there are costs associated with providing them with a service. Unless they are really naive or have only been on the web once or twice before, or maybe been living under a rock somewhere for the past few years, they will be very open to the idea of pitching in to support the site and service that you provide for them.
There are going to be a few naysayers, but they will actually help you out because the ones who want to contribute but need a push will get PUSHED over the edge when the naysayers pipe up. On our site it happens every time. Someone says something about "those silly banners and sponsored by links" I post a reply just reminding people about the costs of providing a kick ass service and forum for them and almost immediately someone else chimes in about invaluable its been for them. Next thing you know, your activity in the forums goes way up and the on-the-fence contributors click that "donate here" button.
Be open about it. Post a message about a subscription option, and explain that "if you like what you get here and would like to help keep it going CLICK HERE." You should also ask what extra things people would like to see as a paid subscriber. One of the premium options can even be to be on your Member Advisory Board. They pay to give you idea
