A clearer idea of the structure:
dispatch_after(when: dispatch_time_t, queue: dispatch_queue_t, block: dispatch_block_t?)
dispatch_time_t is a UInt64. The dispatch_queue_t is actually type aliased to an NSObject, but you should just use your familiar GCD methods to get queues. The block is a Swift closure. Specifically, dispatch_block_t is defined as () -> Void, which is equivalent to () -> ().
Example usage:
let delayTime = dispatch_time(DISPATCH_TIME_NOW,
Int64(1 * Double(NSEC_PER_SEC)))
dispatch_after(delayTime, dispatch_get_main_queue()) {
println("test")
}
EDIT:
I recommend using @matt's really nice delay function.