To simplify things a whole lot...
Epcot, doesn't really matter.
Studios, doesn't really matter.
Animal Kingdom, doesn't really matter.
For the Magic Kingdom, you can either go the commando route or the leisure route. The commando route is probably closest to what you're used to with the legacy system. Get the Fastpasses as early as possible for the biggest rides, crisscrossing the park to get on Mine, Splash, Space, Thunder, and Peter. Then return to the kiosks to get additional Fastpasses.
I think the major benefit of the FP+ system is that it doesn't require commando touring because you don't need a "runner" to crisscross the park. Since FP+, I've always done two full MK days per trip. One day would have FP+ for Space, Mine Train, and Pooh. The other day would have FP+ for Splash, Thunder, and Peter Pan. We'd do half of the park each day with Fastpasses spread throughout.