Keep in mind that "role-playing games" on a forum have little if anything to do with the more traditional "role-playing games" conducted on a tabletop, over root beer and chips, using pencils, paper, and dice. Rather, the forum version is freeform - you only fail at an action if you think it would make more sense dramatically, in the context of the unfolding story. (Unfortunately, this version is also more vulnerable to "munchkinism" than the paper-and-pencil sort - a munchkin can decide that he/she will never fail at anything, and can block any actions directed at him/her.)
Most simply, in the forum version, you assume a character you wish to portray, and interact with the other characters through your posts.
The more traditional sort can also be played in a forum, in which each player either posts their next intended action or emails it to the game-master, and the GM then resolves the actions according to the rules of the game system being used and posts a description of what happened (to which the players respond, and so forth...). This is generally referred to as a "play-by-email", or PBEM, game, and is descended from the slightly-older version using the postal service (that would be "play-by-mail", or PBM).
_________________
Sodium is a metal that reacts explosively when exposed to water. Chlorine is a gas that'll kill you dead in moments. Together they make my fries taste good.