First and foremost... you wait.
Assuming that you applied off the street, the next step is typically getting a call or (most likely) an e-mail from the FAA with a tentative offer for a facility. If you accept it, you'll then go through the "pre-employment process." The FAA has stopped holding the PEPCs so you're stuck with the "traditional" route of this (going to one person at a time over a span of several weeks).
As long as everything checks out there, you'll wait some more.
Eventually, you'll be handed (e-mailed) your Firm Offer Letter and given a date to attend Oklahoma City for FAA Academy.
As for an amount of time, it can vary widely, with one factor being where you want to go. I do know that a lot of facilities in the Western US (primarily the NW US, not so much LAX, etc.) are NOT hiring until FY2011. There are also some facilities in the Central US that are in the same situation.