The cards can be found via the Spawnmenu.
There is a directory system in the botom left of the spawnmenu that is used for models and ragdolls.

Since the cards count as props, Garry's Mod stores them in the botom left folders within the spawnmenu.
To spawn the cards, follow these steps:
1. Open the Spawnmenu [Q by default]
2. In the botom left of the Spawnmenu, select the "add-ons" folder.
3. Scroll down the list looking for the "Yu-Gi-Oh! Virtual Deck" folder.
4. Open the folder and you'll be able to spawn any of the 28 cards currently available in the pack.

The process is similar to spawning props and ragdolls.
So the file directory in the botom left of the spawnmenu should go through these folders:
"Spawnmenu > Add-ons > Yu-Gi-Oh! Virtual Deck Volume 1"

I hope you enjoy the add-on guys, happy dueling!