To qualify, you must have held a PSN, Qriocity or Sony Online Entertainment account on or before May 14, 2011. Each service is eligible to receive different claims, but PSN users are able to receive either one or two games - if you already received a free game in Sony's 2011 "Welcome Back" promotion, you're only eligible for one; if not, you're eligible to choose two - from a list that includes standouts like LittleBigPlanet and God of War HD. Notably, none of the games on offer are for the PlayStation 4. If none of the games tickle your fancy, you can instead choose free dynamic themes for your PlayStation 3 or free PlayStation Plus subscription time.
After wading through multiple pages of bureaucratic legalese, you'll find everything you need to make your claim at the PSN-SOE settlement website.