Apparently, connecting to github via ssh is blocked on the consoles (the alternative route ssh.github.com:443 also does not work anymore).
For connecting via https, github does not allow using the password anymore. Instead, one needs a "personal access token", which can be created here: https://github.com/settings/tokens
The token is then used instead of the password, i.e., pasted or typed into the authentication prompt.
To automate this, the git credential store can be used. Enable it like this:
git config credential.helper storeNext time the "password" (actually the token!) will be asked, it will be stored. Afterwards, it won't be asked again.