Don't apply for the same one as Graham Smith. (glares)

Seriously though, you make yourself known. Practice with a blog or other site, spend some time working the kinks out of your style, and make sure you have some great pieces under your belt - features and reviews rather than opinion pieces are usually best.

Here's the important part: You're not just trying to show off that you can write or know everything about every game that's ever existed, you're showing that you have an interesting, unique voice that's a good fit for the magazine. Obviously, you don't want any typos or grammatical howlers, but typos can be fixed. Your voice can't.

With a magazine as awesome as Gamer, there's always going to be a lot of people competing for space, but the guys who work on it are incredibly nice and always looking for new talent. If you don't get a response, keep trying. Take part on the forum (for the love of god, not posting typo reports and the like - nobody likes a smartarse). Keep writing for other sites so that you can submit your latest masterpieces. Blogs will do, but ideally you want something where someone else will have given it an editing pass and it makes it clear that someone else has considered your work worth publishing.

Also, consider applying for work experience. It's unpaid, but a lot of people have found spending a week in the office a great way to start getting freelance work or becoming a known quantity as and when new full-time gigs open up.