I get this sort of question from time to time:
A 20something friend of mine is interested in getting an entry-level position in the gaming world (just about any aspect, I think).
Do companies have internships, like film companies, where you can prove your worth? Or do you just send queries to companies?
It’s not that easy to get in as “entry level — just about any aspect.” At our company we don’t have jobs for jes’ folks. We have jobs for programmers, and artists, and animators. We have two playtesters, known as Quality Assurance people. They're not entry level, either.
(QA is "playtesting," but it's more like "playing the game repeatedly and trying to break it in every conceivable way. I'm told it's a good niche for people on the autism spectrum, who don't mind a little repetition.)
There are quite a few university programs that teach specific skills: programming, environmental art, animation, etc. The Cégep du Vieux Montréal, for example, has a whole video game program (en français). The video game biz is growing, especially here in Montréal, so a talented and skilled graduate can get a job.
I think most people would tell you to go to game dev conferences and talk to people at companies. If you can't afford a ticket to a conference, you can volunteer, and attend the conference on your off hours. Volunteering is also a good way to meet people.
Personally, I find conferences incredibly daunting. I don't like to go to game dev conferences until I can nab a speaker slot. I have a touch of Asperger's myself. I do better when I have some context; and it's easier to meet people in the speaker's lounge than milling around. If you have deep knowledge in an outside field, you have a shot. E.g. if you are not only a gamer but a retired Special Ops commando, or a copyright lawyer, or a publicist, etc., you can probably think of something to say for half an hour. My ticket to the podium has generally been "lessons from screenwriting."
But, at a minimum, going to conferences give you something to talk about when you do get your foot in the door.
Note that there's a difference between game conventions and game dev conferences. PAX is a game convention. GDC is a game dev conference. The PAX conferences are mostly there so game companies can promote their games to customers. (Also so gamers can meet other gamers and play games on cardboard.) GDC is there so professionals can get learnings and then go out drinking with people they haven't seen since they were all fired.
You can talk to game devs at PAX. At PAX East last year we had the art director, a gameplay designer, an environmental artist, the studio head and the producer, among others. A lot of tiny teams send everybody. Bigger companies send mostly marketing people.
There are game industry sites, e.g. Kotaku and Gamasutra. They have job listings, too. But again, not many “I am an untrained smart person” jobs.
I don't think there are a lot of internships. Showbiz has a use for untrained people. Video game companies don't need anyone to drive the van or man the craft services table.
If any readers out there have better information than the above -- my own trajectory has been pretty idiosyncratic -- please post a reply!