var timer: NSTimer?
var timerStart: NSDate?

func startTimer() {
    // get current system time
    self.timerStart = NSDate()

    // start the timer
    self.timer = NSTimer.scheduledTimerWithTimeInterval(1, target: self, selector: Selector("update:"), userInfo: nil, repeats: true)
}

func update() {
    // get the current system time
    let now = NSDate()

    // get the seconds since start
    let seconds = now.timeIntervalSinceDate(self.timerStart)

    ...
}