There are lots of ways to do search engine optimization on a forum, I will tackle just 10 ways of doing it and as you stay on forums, you'll figure it out yourself. Usually these tips are effective on a vbulletin(tm) forum with vbseo(tm) installed. Forums are communities often updated by member's contributions and are very well seo'ed (search engine optimized) on majority of search engines. So if you have a blog, you're only doing it all alone, in forums people are helping you out with your seo daily practices.
1. Forum signature or commonly called sig
Based on forum policies and tos as well, create your own forum sig optimizing your keyword, for example if it's a dating site you place your forum sig for your dating domains there.
2. Avatar - remote uploads
Those tiny icons or graphics representation/symbol/emblem of yourself, it could be a logo, a photo, or just a made-up cartoon. Use the remote upload where it links to your server's graphics not locally. If allowed on forum put in your domains there if not linking remotely will give hits to your site.