Extract the downloaded zip file.
Open the "Files" folder.
Then move the .dbc files you need in your Football Manager 2013 editor data folder:
Win Vista/7: C:\Users\<username>\Documents\Sports Interactive\Football Manager 2013\editor data\
Win XP: C:\Documents and Settings\<username>\My Documents\Sports Interactive\Football Manager 2013\editor data\
Mac OS X: /Users/<username>/Documents/Sports Interactive/Football Manager 2013/editor data/
Create the folder editor data if it doesn't exist.
Start a new game.
In case you have more editor data files: When setting up a new game, do not have any other data update files ticked on your Editor Data Files screen than the one you want to use.
Files that add new competitions are OK to have.