The primary way to add games to an iPod Touch is by going directly to the iTunes App Store from your computer. Begin by browsing through the iTunes Store, going into the Games subsection from the menu in the upper right hand corner. It stands on its own in the same way that Social Networking and Utilities does. In this area, you can see options such as the most popular paid and free iPod Touch games as well as featured ones. You will also have the choice of looking at sub-categories, such as Simulation or Role Playing Games.
When you find a game that interests you, drag your cursor over it. This gives you two options. First, you can click on the icon or the text to open up its distinct page. Second, you can just select the download button that appears. It is usually best to look at the page unless you are certain you want to download that game.
Once you determine that you want to download the game, you will hit the grey button that lists a price on it, and if it is a free iPod Touch game, then it will simply say Free App on it. From here, a log in request will come up asking for the email and password for your iTunes account. When this is entered successfully, it will charge the credit or debit card that has been assigned to the account and your Apple ID. You will do this before you ever make any purchases from iTunes, and it remains standard unless you want to change it. A receipt will later be sent to the email assigned to the account to list your purchases.
Now that the purchase has been made, it will begin downloading to your computer within iTunes. When it has finished, it will list the new game in the App section of the Library, which is right below books in the left hand panel. Plug your iPod Touch as if you were going to sync it, yet cancel the sync when it begins. Select your iPod Touch and then go into the Apps tab from the middle panel. Make sure that the Sync App box is selected, and then go down the list of apps below and make sure that the game you downloaded is also selected. From here, you will then initiate the sync manually, putting the game onto the iPod.