You can start networking now. I wouldn't start sending out applications earlier than 3-4 months before graduation, but I know others will disagree.

I agree with Tom about networking and when to start applying. There are a couple of other things to bear in mind:

1) Internships are in sync with semesters, permanent jobs are not. Games companies may offer promising interns permanent positions but generally they hire all year round based on project demands. If you have a particular company in mind, keep an eye on what they're up to for clues: if they've just shipped a game it's likely a new project will start ramping up a month or two after. If they've just announced a game, there's a chance they're moving from pre-production into production which can need new staff.

2) Most universities have a computing or games course. Even discounting the people who didn't take it seriously, that's a hell of a lot of new graduates for very few junior jobs and on paper at least most of them look the same - no real job experience and a bunch of education grades. You need to stand out from the crowd - develop some polished portfolio demos that show off your programming abilities - it also makes the interview process a lot easier for both you and for the interviewer because they can ask you questions about technical choices you made and you get to talk about something you know (and get to prove you've not just rote learnt the very basics).