Return true for disabling marker click event
googleMap.setOnMarkerClickListener(new OnMarkerClickListener() {
    @Override
    public boolean onMarkerClick(Marker marker) {
        return true;
    }
});
For getting click on maps use this listener on onMapReady
@Override
public void onMapReady(GoogleMap googleMap) {
googleMap.setOnMapClickListener(new GoogleMap.OnMapClickListener()
{
    @Override
    public void onMapClick(LatLng arg0)
    {
        Log.v("onMapClick", "Yea worked!");
    }
});
}
Complete code
public class MapsActivity extends FragmentActivity implements OnMapReadyCallback {
private GoogleMap mMap;
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_maps);
    // Obtain the SupportMapFragment and get notified when the map is ready to be used.
    SupportMapFragment mapFragment = (SupportMapFragment) getSupportFragmentManager()
            .findFragmentById(R.id.map);
    mapFragment.getMapAsync(this);
}
/**
 * Manipulates the map once available.
 * This callback is triggered when the map is ready to be used.
 * This is where we can add markers or lines, add listeners or move the camera. In this case,
 * we just add a marker near Sydney, Australia.
 * If Google Play services is not installed on the device, the user will be prompted to install
 * it inside the SupportMapFragment. This method will only be triggered once the user has
 * installed Google Play services and returned to the app.
 */
@Override
public void onMapReady(GoogleMap googleMap) {
    mMap = googleMap;
    // Add a marker in Sydney and move the camera
    LatLng sydney = new LatLng(-34, 151);
    mMap.addMarker(new MarkerOptions().position(sydney).title("Marker in Sydney"));
    mMap.moveCamera(CameraUpdateFactory.newLatLng(sydney));
    googleMap.setOnMapClickListener(new GoogleMap.OnMapClickListener() {
        @Override
        public void onMapClick(LatLng latLng) {
            Toast.makeText(MapsActivity.this, "Map clicked", Toast.LENGTH_SHORT).show();
        }
    });
    googleMap.setOnMarkerClickListener(new GoogleMap.OnMarkerClickListener() {
        @Override
        public boolean onMarkerClick(Marker marker) {
            Toast.makeText(MapsActivity.this, "Marker disabled", Toast.LENGTH_SHORT).show();
            return true;
        }
    });
  }
}