All of the wild pack, Maddy and her parents, and Rhydian can transform in the series because they are Wolfbloods. In the leader of the pack, we learn, from Shannon, that transformation isn't instantaneous. You normally start transforming at the age of 14. Furthermore you can't do eolas until you transform. Transformation doesn't hurt and is completely normal for a wolfblood. After transformation you gain extra energy from fullmoon causing you to be more feral, or want to run a marathon in your sleep....
You don't actually see it take place. But you do see how it impacts the body from the inside and changes the DNA from the veins. The transformation can be caused by emotions but when you control it you can transform whenever you want to.
Here we see Maddy transform for the first time in episode 5 Occam's Razor of season 1.
transformation in the den at full moon