TL;DR version: You start with the regular slot at level 1. Every 10 levels you gain an additional slot on your primary and secondary powers (at 50, all powers would be 6 slotted). With the power pools and ancillary/epic, you gain additional slots through missions that you complete (easy for the first, with increased effort for later slots).
Alternate TL;DR; Each power you choose would be leveled by use (gaining a slot every 10 levels)(with passives gaining slots over time), so powers used more often would gain slots faster (Long recharges have a different formula, to keep things fair).
Having it done by use would level the playing field (casual Vs power-leveled character) in certain ways. I can see the advantage of fast recharge getting to cap easier compared to slower recharge powers. A remedy could be that the powers you use to gain experience (active, passive, toggle) get a portion of the experience. For the casual player (less than 4 hours a week), there would be an offline accrual (yes, like day jobs) that if a character is offline X days (or enough hours), that they would gain a slot to any power they wish. With a max of 1 slot accrued at a time (can't gain another until it is used), this would give some progression to those that don't play a lot. After everything is 6-slotted, your character would stop gaining slots.