Every Alliance may build ONE Alliance HQ. The HQ can only be built by the Alliance Marshal.
If you are the Alliance Marshal, to build your Alliance HQ, you must:
1. Open the Map and tap on the "Build Alliance HQ” button. Then, find a suitable location for your HQ and tap the green tick to place it.
Or
2. Go to the "My Alliance" tab at the Alliance Center and tap the "Build Alliance HQ" button near the top of the screen. This will take you to the map.