As a new player you are automatically assigned to an alliance.
Note on new maps with closed bridges: If you find yourself on a new map where all bridges are still closed, you can only leave your alliance 3 days after all bridges are open! This ensures that everyone can build up at their leisure during the closed bridges.
If you want to change the alliance, click on the "Alliance" tab in the game menu and then on "Overview". At the bottom left of the table you will then see the red button "Leave Alliance".
Attention: if you are not a new player anymore and already have a few points (over 2000) there is a 72 hour ban as "mutiny protection". If you click on "Leave Alliance", your bases will be outlined in red so that your alliance friends can see that you want to leave the alliance and their vehicles that may be parked in front of your base stations can be brought to safety. You can leave the alliance faster if a leader or co-leader confirms your request to leave (and kicks you out, so to speak).
After clicking on this button / when you have left the alliance, you are without an alliance and can either form a new alliance ("Form Alliance") or join an existing alliance ("Select Alliance") by clicking on the "Alliance" tab. If you want to join an alliance, you will see in the table all existing alliances that accept newcomers. By clicking on the "Select Alliance" button in the column on the right you can choose your desired alliance.