It's totally normal to ask where people work. In fact, it's outright good to do. As you meet more people, you'll find odd coincidences, like someone you just met works with a good friend of yours. Things like this will help build your network, and that's a good thing, especially as you look for a job. And don't forget to maintain your network once you've gotten the job!
As an example: "Hey, how's it going?"; "What brings you here"; "Oh cool, do you use this at work?"; "What company do you work with?"; and you're there in 4 sentences.
In social chit-chat, it's .. awkward? to bring it up, sometimes. I'd guess that maybe 1/20 people know anything about what I do. Mention [Puppet, Solaris, Linux, BASH, Ruby, NetApp, FTP] and their eyes glaze.