I think we have more better version to enable the location without opening the settings just like google map works.

It will looks like this -

Add Dependency in gradle - compile 'com.google.android.gms:play-services-location:10.0.1'

public class MapActivity extends AppCompatActivity {

    protected static final String TAG = "LocationOnOff";

 
    private GoogleApiClient googleApiClient;
    final static int REQUEST_LOCATION = 199;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        this.setFinishOnTouchOutside(true);

        // Todo Location Already on  ... start
        final LocationManager manager = (LocationManager) MapActivity.this.getSystemService(Context.LOCATION_SERVICE);
        if (manager.isProviderEnabled(LocationManager.GPS_PROVIDER) && hasGPSDevice(MapActivity.this)) {
            Toast.makeText(MapActivity.this,"Gps already enabled",Toast.LENGTH_SHORT).show();
        }
        // Todo Location Already on  ... end

        if(!hasGPSDevice(MapActivity.this)){
            Toast.makeText(MapActivity.this,"Gps not Supported",Toast.LENGTH_SHORT).show();
        }

        if (!manager.isProviderEnabled(LocationManager.GPS_PROVIDER) && hasGPSDevice(MapActivity.this)) {
            Log.e("TAG","Gps already enabled");
            Toast.makeText(MapActivity.this,"Gps not enabled",Toast.LENGTH_SHORT).show();
            enableLoc();
        }else{
            Log.e("TAG","Gps already enabled");
            Toast.makeText(MapActivity.this,"Gps already enabled",Toast.LENGTH_SHORT).show();
        }
    }


    private boolean hasGPSDevice(Context context) {
        final LocationManager mgr = (LocationManager) context
                .getSystemService(Context.LOCATION_SERVICE);
        if (mgr == null)
            return false;
        final List<String> providers = mgr.getAllProviders();
        if (providers == null)
            return false;
        return providers.contains(LocationManager.GPS_PROVIDER);
    }

    private void enableLoc() {

        if (googleApiClient == null) {
            googleApiClient = new GoogleApiClient.Builder(MapActivity.this)
                    .addApi(LocationServices.API)
                    .addConnectionCallbacks(new GoogleApiClient.ConnectionCallbacks() {
                        @Override
                        public void onConnected(Bundle bundle) {

                        }

                        @Override
                        public void onConnectionSuspended(int i) {
                            googleApiClient.connect();
                        }
                    })
                    .addOnConnectionFailedListener(new GoogleApiClient.OnConnectionFailedListener() {
                        @Override
                        public void onConnectionFailed(ConnectionResult connectionResult) {

                            Log.d("Location error","Location error " + connectionResult.getErrorCode());
                        }
                    }).build();
            googleApiClient.connect();
         }

         LocationRequest locationRequest = LocationRequest.create();
            locationRequest.setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY);
         locationRequest.setInterval(30 * 1000);
         locationRequest.setFastestInterval(5 * 1000);
         LocationSettingsRequest.Builder builder = new LocationSettingsRequest.Builder()
                    .addLocationRequest(locationRequest);

         builder.setAlwaysShow(true);

         PendingResult<LocationSettingsResult> result =
                    LocationServices.SettingsApi.checkLocationSettings(googleApiClient, builder.build());
         result.setResultCallback(new ResultCallback<LocationSettingsResult>() {
            @Override
            public void onResult(LocationSettingsResult result) {
                final Status status = result.getStatus();
                switch (status.getStatusCode()) {
                  case LocationSettingsStatusCodes.RESOLUTION_REQUIRED:
                       try {
                           // Show the dialog by calling startResolutionForResult(),
                           // and check the result in onActivityResult().
                                status.startResolutionForResult(MapActivity.this, REQUEST_LOCATION);
                       } catch (IntentSender.SendIntentException e) {
                           // Ignore the error.
                       }
                       break;
                 }
             }
         });
     }

}

All these answers are not allowed now. Here is the correct one:

For all those still looking for the Answer:

Here is how OLA Cabs and other such apps are doing it.

Add this in your onCreate

if (googleApiClient == null) {
    googleApiClient = new GoogleApiClient.Builder(this)
            .addApi(LocationServices.API).addConnectionCallbacks(this)
            .addOnConnectionFailedListener(Login.this).build();
    googleApiClient.connect();
            LocationRequest locationRequest = LocationRequest.create();
    locationRequest.setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY);
    locationRequest.setInterval(30 * 1000);
    locationRequest.setFastestInterval(5 * 1000);
    LocationSettingsRequest.Builder builder = new LocationSettingsRequest.Builder()
            .addLocationRequest(locationRequest);

    // **************************
    builder.setAlwaysShow(true); // this is the key ingredient
    // **************************

    PendingResult<LocationSettingsResult> result = LocationServices.SettingsApi
            .checkLocationSettings(googleApiClient, builder.build());
    result.setResultCallback(new ResultCallback<LocationSettingsResult>() {
        @Override
        public void onResult(LocationSettingsResult result) {
            final Status status = result.getStatus();
            final LocationSettingsStates state = result
                    .getLocationSettingsStates();
            switch (status.getStatusCode()) {
            case LocationSettingsStatusCodes.SUCCESS:
                // All location settings are satisfied. The client can
                // initialize location
                // requests here.
                break;
            case LocationSettingsStatusCodes.RESOLUTION_REQUIRED:
                // Location settings are not satisfied. But could be
                // fixed by showing the user
                // a dialog.
                try {
                    // Show the dialog by calling
                    // startResolutionForResult(),
                    // and check the result in onActivityResult().
                    status.startResolutionForResult(Login.this, 1000);
                } catch (IntentSender.SendIntentException e) {
                    // Ignore the error.
                }
                break;
            case LocationSettingsStatusCodes.SETTINGS_CHANGE_UNAVAILABLE:
                // Location settings are not satisfied. However, we have
                // no way to fix the
                // settings so we won't show the dialog.
                break;
            }
        }
    });
}

These are the implmented methods:

@Override
public void onConnected(Bundle arg0) {
    // TODO Auto-generated method stub

}

@Override
public void onConnectionSuspended(int arg0) {
    // TODO Auto-generated method stub

}

@Override
public void onConnectionFailed(ConnectionResult arg0) {
    // TODO Auto-generated method stub

}

Here is the Android Documentation for the same.

This is to help other guys if they are still struggling:

Edit: Adding Irfan Raza's comment for more help.

@Override protected void onActivityResult(int requestCode, int resultCode, Intent data) {
     if (requestCode == 1000) {
         if(resultCode == Activity.RESULT_OK){
             String result=data.getStringExtra("result"); 
         } if (resultCode == Activity.RESULT_CANCELED) {
             //Write your code if there's no result 
         } 
    } 
} 

Full example :

/**
 * Function to check if best network provider
 * @return boolean
 * */
public boolean canGetLocation() {
    return this.canGetLocation;
}

/**
 * Function to show settings alert dialog
 * */
public void showSettingsAlert(){
    AlertDialog.Builder alertDialog = new AlertDialog.Builder(mContext);

    // Setting Dialog Title
    alertDialog.setTitle("GPS is settings");

    // Setting Dialog Message
    alertDialog.setMessage("GPS is not enabled. Do you want to go to settings menu?");

    // Setting Icon to Dialog
    //alertDialog.setIcon(R.drawable.delete);

    // On pressing Settings button
    alertDialog.setPositiveButton("Settings", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog,int which) {
            Intent intent = new Intent(Settings.ACTION_LOCATION_SOURCE_SETTINGS);
            mContext.startActivity(intent);
        }
    });

    // on pressing cancel button
    alertDialog.setNegativeButton("Cancel", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which) {
        dialog.cancel();
        }
    });

    // Showing Alert Message
    alertDialog.show();
}

Here is the doc : http://www.androidhive.info/2012/07/android-gps-location-manager-tutorial/ (copied point 7)