Hi the best way would be to use google adsense - possibly use clickbank if the forum relates to clickbank products
Maybe you can advertise someone's link or business in your signature and post a lot. That may be an option.
Create a good forum with a good following. Then slowly increase the amount of Advertising, whether that be through Google Adsense or affiliate schemes always keeps the ads targeted to your niche and not too much of it to steer customers away.
I've always loved forums, and I kinda would like to have one. Has anybody had a good experience doing link sales from forums they own? Is there any demand for it or do people prefer not to purchase links on forums? I know people usually become ad blind so it's sometimes hard to monetize. Direct sponsorship is probably the best option I would think either through banners or perhaps link sales.
participate in a particular forum according to your interest and then try to give solutions of problems. Once your profile establish strongly then you have to opportunity to earn money.