How does a substance's temperatura chanté when the average kinetic energy of its particles increases? when it decreases?

Kinetic energy means movement. This means that the more something moves, the more kinetic energy it will have! And the faster something moves, the more heat it produces! Altogether, this means that the more Kinetic energy something has, the hotter it will be!

The opposite is also true. The less something moves, it will have less Kinetic energy and the colder it will get. 

If you're having trouble understanding this, think of it like how the particles in water move compared to how the particles in ice move. The particles in water are free flowing and can move wherever they want. If they get colder, they won't move as much, and eventually they'll stop flowing around, forming a solid and staying colder than the water will get.