How do I (self) promote a board game?
First you'll want to build up a fan base.  To do that, you could:


Introduce it at board game meetups and conventions.
Send print and play files to interested people over the internet.
Show it off on board game forums.


Once you have a fan base, then it's time to think about options for publishing the game.  I wouldn't recommend spending any money on marketing until you have a publishing route worked out, since you won't have a product to sell yet, and (depending on which way you go) your publisher will probably already have their own marketing ideas and budget.