Ok, Fedora adheres, thankfully, to the FHS a lot and, thus, changes where things might go. In this case, they don't use the git user; they use gitolite3 as a user. And, in a nutshell, here's how to configure it:
The first part of the HowTo goes on the Server:
# Become root
su -
# Install gitolite3
yum -y install gitolite3
# Become the gitolite3 user
su - gitolite3
# Copy the public part of the key you're going to use to manage this gitolite instance (from your workstation).
# Obviously, this has to be a single line and no spaces. This is, normally, the source of all problems: badly formated keys
cat < < 'EOF' > renich.pub
ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAAEAQC8LgmK... My Workstation Key
'EOF'
# set it up
gitolite setup -pk renich.pub
Now, from your Workstation:
git clone gitolite3@host:gitolite-admin
That is dead simple! Just do it and have your own gitolite3 instance!
Now, read the manuals in order to get literate about it's management and configuration:
References
ACK
Thanks, John Hall, for the correction ;)
Thanks, John, for the correction on the clone command as well.