How to rotate/translate a part of body without afecting the rest of it? Hello Blender wizards,

I've been following a really old tutorial (2009): https://www.youtube.com/watch?v=sUifORl-faI and I've come to a problem.

When I try to rotate just the extrusion, the rest of the body rotates as well (7:36 to 7:41).
A similar problem occurs when I try to translate just a single vertex, and all other vertices move together (9:05 to 9:10).

Thanks!
You must have activated the Proportional Editing option on the bottom horizontal menu bar. It allows you to influence the closest vertices/edges/faces.