The simplest way to do this is to use the package manager to install the MythTV package. Unfortunately, with the default Mint pacakge sources, the Mint packages are often one or more versions/revisions behind the current stable MythTV builds.
The best source for latest builds of MythTV for Mint are the MtyhBuntu repositories .
However, you can't just add the MythBuntu repositories as the package updater doesn't think Mint is Ubuntu so it will fail. Now, strictly speaking, Mint isn't Ubuntu, but its Ubuntu based so the MythBuntu builds work perfectly. To get this to install properly, we need to trick the package manager into thinking we are running Ubuntu. Once the repositories are loaded we can reverse the changes.
To trick the installer into thinking we are running Ubuntu, we need to edit /etc/lsb-release and change the 'DISTRIB_CODENAME=julia' to 'DISTRIB_CODENAME=maverick'.
'julia' is the name the Mint developers refer to Mint 10 by and 'maverick' is the name that the MythBuntu repositories refers to the version of Ubuntu (10.10) that Mint 10 is based on.
Once the MythBuntu sources are added into the package manager you can reverse the above change.
Notes
Mint 11 is based on Ubuntu 11.04. If you have problems finding specific Mint 11 solutions, then search for Ubuntu 11.04 solutions as most of these will apply to Mint 11 as well.