Go into /etc/yum.repos.d/, and carefully look at all of the files in there.
For each file that points to a CentOS repository, disable it by setting
enabled=0, and make a copy that points to the CentOS 6.3 repo directories on vault.centos.org. Any directory with a "repodata" subdirectory is usable as a yum repository directory.
You'll probably at least want:
name=CentOS 6.3 - $basearch
name=CentOS 6.3 Updates - $basearch
Note that you won't get any security updates that came out since CentOS 6.4 was released. If you install the
yum-plugin-security module, you may be able to use commands like
yum --enablerepo=centos --security update-minimal to pull in just the security updates, but I have not checked that, and have not even verified the yum repository names.