Since it looks like you are using Debian. You just need to get the appropriate packages (.deb's) must Debian based distros have a package manager that is configured with varios Repositories. So the first theing to do is use your package manager to search for the Mame packages.
If you don't see then in the package manager you may need to add/enable other repositories such as the marillat repositories which you can find some info on here
if you are very new to using/setting up your package manager you may want to talk to someone more familiar with your peticular distro on what are the best repositories to add and of course make sure you add the repositories that are correct for your arcitecture. (ie don't add PPC repositories is you are using a x86 system)
you can also get some info on apt and apt-get here:
hope this helps
please do be a little cautious in adding repositories as adding the wrong ones can cause version conflicts in your package-management system.