Basically there will be a total of 11 Upgrade Paths. Each class will have two unique paths for a total of 8 paths for them. The other 3 paths are all-kit, meaning any kit can use them. Each path has 4 Specializations each meaning there would technically be a total of 44 Specializations in the game.
While thats not necessarily true, as paths will reuse specializations, DICE has confirmed there would be over 25 Specializations in the game. Paths work based on Squad based actions, with progress gained to each specialization in a path by doing them. Progress for a path is saved if a new path is chosen, a new squad has been joined, or a new kit has been selected. Some progress, however, will be lost for the path currently selected if your entire squad has been wiped.
The post on the BF Blog detailing this can be found at: http://blogs.battlefield.com/2013/08/road-to-bf4-field-upgrades/