For those who really only want to draw a simple line – there is indeed also the short short version.
GoogleMap map;
// ... get a map.
// Add a thin red line from London to New York.
Polyline line = map.addPolyline(new PolylineOptions()
.add(new LatLng(51.5, -0.1), new LatLng(40.7, -74.0))
.width(5)
.color(Color.RED));
from https://developers.google.com/maps/documentation/android/reference/com/google/android/gms/maps/model/Polyline