OSMDroid is terribly documented, but the way they designed it makes it very flexible and self-explanitory if you look at the implementable methods. Here is how you use Mapbox tiles with OSMDroid as of January 2015.
mvMap = (MapView) rootView.findViewById(R.id.mapview);
String mapCode = "mapbox.streets";
final String accessToken = "myAccessToken";
OnlineTileSourceBase customTileSource = new XYTileSource("MapBoxSatelliteLabelled",
ResourceProxy.string.mapquest_aerial, 1, 19, 256, ".png", new String[]{
"http://a.tiles.mapbox.com/v4/" + mapCode + "/",
"http://b.tiles.mapbox.com/v4/" + mapCode + "/",
"http://c.tiles.mapbox.com/v4/" + mapCode + "/",
"http://d.tiles.mapbox.com/v4/" + mapCode + "/"}){
@Override
public String getTileURLString(MapTile aTile) {
String str = super.getTileURLString(aTile) + "?access_token=" + accessToken;
return str;
}
};
TileSourceFactory.addTileSource(customTileSource);
mvMap.setTileSource(customTileSource);
Quick tip: If you're using Android Studio, use break points to get the value of any variable. This helps with debugging and understanding unfamiliar code. That's how I figured out that getTileURLString() returns the full URL of the tile.