Hi Larry,
as MV has pointed out already; Zorin is based on Ubuntu which in turn is based on Debian.
Any packages/programs that you wish to download and install can be done using the Ubuntu Software Center, Synaptic package manager or using the terminal if you know the commands.
Any 3rd party packages that you might want to install should end with ".deb" or "all.deb" and should downloaded from a known and verified source/location, in other words; a place that you know is safe to download from, a good example would be adobe.com or the google earth website.
It is also important to note that you should make sure that you download the correct package for your PC, either 32 bit; or 64 bit, packages ending "all.deb" work with both systems!!.
There are also "tar" files which you can always use providing you follow the instructions given with each package!!. (safety rule applies here too!)
Do not try and use "rpm" packages if you possibly can as they are designed for another type of packaging system!. (Redhat Package Manager)
Regards Wolfman
See this thread also:
viewtopic.php?f=6&t=1778&p=6447#p6447