How can I make vertices on a cylinder create a circle (like in this tutorial https://youtu.be/cHbOCSkqmo8?t=2m43s) ?
Activate the Loop Tools add on in User Preferences (Ctrl+Alt+U). Apply the transformations to the object (Ctrl+A-->Rot&Scale). Select the edges on a cylinder you want to transform to a circle and snap the cursor to it (Shift+S). Press W-->LoopTools-->Circle. Finally uncheck the Flatten checkbox in a Circle panel of a Tool Shelf (T).