Every time you master a new skill on Sumdog, your pet will learn a new trick.
On the City page, the skill you're currently working on is shown at the top of the screen. Whenever you play games, you will be asked questions about that skill. The progress bar shows you how close you are to mastering that skill.
Once you complete the skill you will be given a new trick for your pet to perform.
The coloured buttons show the tricks your pet has already learned and the grey buttons show the tricks your pet still has to learn. Select a coloured one and the pet will perform the trick.