How to install tailscale in Alpine Linux

My recommendation is to just use the community repository:

echo http://dl-2.alpinelinux.org/alpine/edge/community/ >> /etc/apk/repositories
apk add -U tailscale

Now you need to add tailscaled to the autostart list and then start the service so you can use it right now:

rc-update add tailscale
/etc/init.d/tailscale start