Heh, that was the first thing that came to mind too.
GaryV definitely has that kinda thing down packed.
Shortened version for people too lazy to watch video, Type in keywords appropriate to your site in Google etc, look at the ads in the sidebar and approach those companies directly.
I guess "sponsorship" is really a nice word for "self-managed brand advertising." It's semi-popular in the development blogging world. For example, you'll see Peepcode banners on many Ruby blogs.
Let's say you run a .Net blog and a .Net tools vendor wants their logo on the sidebar of your blog. You say, sure, it costs $500 per month (or whatever) and that's it. If you've got the readership, fame, or whatever, it's reasonably easy. You won't get an awesome CPM but it's nice to have known companies supporting you.
How does that work, exactly? Do you mean, you put links on your page to those other key companies and then get paid per click?