My gut reaction to the news that certain games would be "upgradable" to their next-generation counterparts, whether that be on Xbox One or PlayStation 4, was that the savings had better be significant. And they are! If you buy Battlefield 4, Watch Dogs, Call of Duty: Ghosts, or Assassin's Creed IV: Black Flag on PS3, you'll be able to get the same title on PS4 for a mere $9.99. Sony has detailed the digital upgrade process today.
Disc-based PS3 versions of those games will include a redeemable code, and you'll also need to keep the discs themselves to play the PS4 versions. However, if you're going the all-digital route by purchasing through the PlayStation Store, there's no code redemption -- the PS4 versions will simply show up on the PS Store with the discounted pricing. That sounds like the way to go.
Another concern was how limited this limited-time promotion would be. The dates to keep track of are: January 31, 2014 (Assassin’s Creed IV and Watch Dogs), March 28 (Battlefield 4), and March 31 (Call of Duty: Ghosts). Redeem your code -- which can be done on PS3, by the way -- and purchase the PS4 versions before those days.
How to Upgrade Select PS3 Games to Their PS4 Versions [PlayStation Blog]