Best way to promote a discussion forum

Clear introduction of each participant by name and profession

Each participant opens with short summary of his/her position

Each participant is given equal time to express and develoop his/her opinion

No personal attacks; no gross language

Each participant is given equal time to summarize the discussion.

First of all, you need to make sure that your forum is targeted to a certain topic.

Based on my personal experience, the best way to promote a website about anything, is by getting as many quality backlinks as possible to the website.

One of the best way to get these quality backlinks is by using the article marketing method. 

You can do this yourself if you are confident with your writing skill. Or else, you should hire professional article writers with SEO knowledge to handle it for you. 

Do you already have a website or are you looking at creating one?  If you already have a website then encouraging your visitors to join your forum shouldn't be too hard.  If are creating a forum from scratch you will need to decide what you want your forum and target that segment - join groups to promote your forum, making sure you have enough posts and replies to post to keep people interested - a lot of people will join a forum if they see that it is popular.