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Depending on the app / game it should move a little or a lot of it if you instruct it to. The main app will remain on the device, but create links to where chunks of the rest of the app is located on the sd card.
So if you need to change cards or wipe it, it's best to move any app segments back to the device first. Sadly some cards can fail quickly or corrupt. If you have a genuine SanDisk or Samsung card they are the best, but hopefully any card will last a year or more. My Kingston lasted 18 months.
So go to Settings, look for Apps or Applications Manager, scroll across to the All (or even SD Card) column, find the game alphabetically, touch to open the App Info screen, and you will find a Move to SD Card option. If it is greyed out, that app is not designed to work with an SD Card.
This is what it looks like on a Samsung:

