I am trying to use location services in my iOS app but for some reason requestWhenInUseAuthorization is not working. When the user first uses the app, the promp         
        
First you need to add NSLocationWhenInUseUsageDescription or NSLocationAlwaysUsageDescription(if you want to use in background) in your info.plist file. See the following image:

Next, in your swift file, you need to call either locationManager.requestWhenInUseAuthorization() or     locationManager.requestAlwaysAuthorization() in your viewDidLoad() method. 
Finally, you can do a mapView.camera = GMSCameraPosition(target: locations.last!.coordinate, zoom: 15, bearing: 0, viewingAngle: 0) in your locationManager delegate method.
Sample code:
class ViewController: UIViewController, CLLocationManagerDelegate {
    var locationManager = CLLocationManager();
    override func viewDidLoad() {
        super.viewDidLoad()
        // Do any additional setup after loading the view, typically from a nib.
        var camera = GMSCameraPosition.cameraWithLatitude(-33.86,
            longitude: 151.20, zoom: 6)
        var mapView = GMSMapView.mapWithFrame(CGRectZero, camera: camera)
        mapView.myLocationEnabled = true
        self.view = mapView
        locationManager.delegate = self
        locationManager.distanceFilter = kCLDistanceFilterNone
        locationManager.desiredAccuracy = kCLLocationAccuracyBest
        if #available(iOS 8.0, *) {
            print("iOS >= 8.0.0")
            locationManager.requestAlwaysAuthorization()
        }
        locationManager.startUpdatingLocation()
    }
    override func didReceiveMemoryWarning() {
        super.didReceiveMemoryWarning()
        // Dispose of any resources that can be recreated.
    }
    func locationManager(manager: CLLocationManager!, didUpdateLocations locations: [AnyObject]!) {
        println(locations.last)
        var mapView = self.view as! GMSMapView
        mapView.camera = GMSCameraPosition(target: locations.last!.coordinate, zoom: 15, bearing: 0, viewingAngle: 0)
    }
}
You can will this post, for more details about LocationManager change in iOS 8.