This documentation has the goal of showing how a user can use the official Android Tailscale client with headscale.
Install the official Tailscale Android client from the Google Play Store or F-Droid.
Ensure that the installed version is at least 1.30.0, as that is the first release to support custom URLs.
After opening the app, the kebab menu icon (three dots) on the top bar on the right must be repeatedly opened and closed until the Change server option appears in the menu. This is where you can enter your headscale URL.
A screen recording of this process can be seen in the tailscale-android PR which implemented this functionality: tailscale/tailscale-android#55
After saving and restarting the app, selecting the regular Sign in option (non-SSO) should open up the headscale authentication page.