If you frequently have to set up git version control system for existing projects then you would very likely run into the problem of having to remove files, which should not have been in git, from git after they were added. Running a git rm will only delete the file from the head and the file would still remain in the repository. This may be alright for small files but this could be troublesome for large files as these would unnecessarily bloat the git repository. But don't worry git being a 'swiss army knife' of version control systems there is a solution to delete files permanently from both your local and remote git repositories.
Do note that this is not a newbie solution and you have to do your bit of reading up on these commands and their implications before you actually run this on a production repository. Also note that you have to have RW+ permissions on the repository to do non-fast-forward pushes
CD to your local working folder and run the following command
git filter-branch -f --index-filter "git rm -rf --cached --ignore-unmatch FOLDERNAME" -- --all
replace FOLDERNAME with the file or folder you wish to remove from the given git repository.
Once this is done run the following commands to clean up the local repository
rm -rf .git/refs/original/
git reflog expire --expire=now --all
git gc --prune=now
git gc --aggressive --prune=now
Now push all the changes to the remote repository
git push --all --force
This would clean up the remote repository.
Now you will have to recreate the .git folders of all the working copies of the repository. This would include cloned repositories by other developers or the cloned repositories at the live and dev sites. You can do this by cloning the repository afresh into a temporary folder and the move the .git folder from the newly cloned repository to the local repository after deleting the existing .git folder from in there. Do remember to checkout the same branch as is already checked out in the local repository in the temporary repository before you move the .git folder to the local repository.
Remember to make a backup copy of the latest repository and the latest local files before you do any of these things so that you can fall back to a working repository if you run into issues.
Do this if you are confident of your git capabilities or else call up the experts :-). Let us know and we will be happy to offer our offshore Drupal development services to help you maintain your server and your repositories.