I'm going with Smells here, but modified. Invite him out to talk about work prospects in general, advice about how to look for a job in the field. It makes someone feel important if you ask them for advice. And then it would naturally come up to talk about how cool his company is, and what would you have to do to specifically work there.
I also wouldn't Facebook him, but I think communicating by email is completely appropriate for a web job. I would email him to ask to set up a lunch. Personally I am always weirded out by people who try to phone me without setting it up by email first. What century do they live in? For a job like that you don't want to give the impression that you don't know how to use the internet.
I don't agree with calling him out of the blue and putting him on the spot. That will make him uncomfortable and no one wants to work with someone who makes them uncomfortable. I don't see the value of bullying him into giving some kind of answer right away - you can't bludgeon someone into giving you a job.
Again, maybe this differs in different fields, but I've worked in a lot of vastly different jobs and there isn't one of them where I could have bettered my chances of being hired by calling someone without warning.