First, log into your account.
Second, in the header section click on "Games" (it's between "Reviews" and "Videos").
Third, you can either type in the name of the game (in whole or in part) or you can enter the console, publisher, developer, or some combination thereof.
From the next screen, find and select the game you own.
Scroll down a bit, and on the left hand side you'll find a box labeled "Community Stats." These are other VGCharterz who own, want, and are currently playing the game. At the top of the box, you'll see a line that says "Owners." Next to it is a number, and next that THAT is a small button labelled "(Add)." Click on that, and the game will go to your collection.
Note that if you ever want to remove the game, simply repeat these steps. Where it used to say "(Add)," it should now say "(Remove)." Click on that button to remove the game from your collection.
You can also do this from your profile. Go to "My Games" under the Quick Links area, find the game you want to delete, and click on "delete", which you'll find right under the game's artbox.