TOTALLY Smoke-challenged

I've never had a Brinkman, but this looks more like a grill that needs a firebox.  If you look on the sides, are there perforated areas that look like something could attach to it?  You might look around the site here to see whether anyone else has the same style, and see what they have to say about it.

Meanwhile, don't let it stop you from trying your first smoke.  You can burn your wood on the side opposite the smoke stack and your meat on the other side.  You'll probably find some posts on here that will help you learn how to do that.  

Be careful, though, because if you do it right, you won't ever quit.  Be sure this is a path you want to go down.  Then just have fun with it.

Welcome and what "ikinya6" said!!