There is no formal application process. Your best bet is to get referrals from our founders and/or mentors.
Pro tip: don't just ask them for a warm intro to us. Get them engaged in your business -- get their advice and use their expertise. If they're excited about your startup, we might be too.
actually, 500 Startups now has a limited application process for our Fall 2012 Accelerator program -- you can now apply on Angel List here: http://angel.co/500startups
As of this upcoming batch, we are now accepting applications via AngelList at 500 Startups. The application period has closed for this batch. However, we anticipate opening up applications for the Fall 2013 batch sometime in August.