Best ways to promote a new forum?

[frank]

First of all you will have to build content if you want to succeed in your promotion campaign.
And in order to promote your forum start posting in other forums of your niche. Build authority, promote your own forum with the signature, once you have build trust people will come looking for your forum.
Another way to fasten the promotion process is to use ad networks. Start using facebook sponsored ads they are much cheap and easy to use but yet very effective.
Try guest posting in your niche blogs. In this way you will build authority along with good backlinks.
Engage & establish a relation with your audience in mass query platforms such as Yahoo answers or Quora.