Instructions
Play games. Nearly every arcade game from the game marketplace and many retail games come with free logos. The logos' prerequisites vary from game to game. However, some games just give you the logos off the bat, but you can only obtain some other logos after earning a specific in-game achievement. For example, "Trials HD" only gives you a certain logo after you beat all of the Extreme difficulty tracks.
Purchase additional logos from the game marketplace. These are logos that are generally never given to you for free in a game and can only be purchased through the store within the console. For example, "Call of Duty" logos are only for sale, not for in-game redemption.
Select your profile under "My Xbox" on your console. Select "Edit Profile," followed by "Change Picture." Select the picture you want to use it.