I run a forum (http://supersmashbc.com) and would like to target certain keywords. What exactly is the best way to do this? I have read several posts, blogs, etc. about how to target certain keywords for other types of sites, but many of the directions are not relevant to forums.

well, people are going to write thread and posts on your forum. They will create the content themselves and target the keywords linked to your niche

Well, one of the key phrases I am trying to get to number 1 at is "Super Smash Bros. Brawl clan." In our forums members use those words all the time, and my site has decent statistics, yet I'm still ranked behind some sites that have very little traffic and very few backlinks.

For example, the number 2 search result is a youtube video that only has 600 views. I know it is youtube, but I get more visitors in 1 day that it has had over its lifetime. I know it isn't all about traffic, but as I said above, my members talk plenty about clans, and I have a decent number of backlinks (compared to my competition in these search results).

For keywords selection
* Be creative, but be choosy.
* Try not to target keyword phrases that are too competitive.
* If there are unusual words associated with your content that you think people might search for, or misspellings, include them sparingly.
* Be specific and only check the keywords that are important to you

Thanks, but I'm not having any problem selecting a keyword. I have a few that I want to target that aren't too competitive and get a decent amount of searches, plus relate to my site perfectly. The problem is I am having problems actually targeting them for my forum.

write some posts using the words / phrases you what to target.

Forums are still websites.

You don't seem to have had a problem deciding what to put in your signature here!