In the manual pages about version control I find the instructions on how to create and switch to branches, also for Git repositories. But I can't find information on how to delete a branch – both locally and remotely – in a Git repository.
Which commands should I use? or is it not possible with Emacs' built-in version-control?
VC’s support for branch operations is currently fairly limited. For decentralized version control systems, it provides commands for updating one branch with the contents of another, and for merging the changes made to two different branches (see Merging Branches).... You may have to do these things from the command line.