Complete newbie, all vertices moving instead of the 3 I selected, not proportional editing https://youtu.be/tt-Y8rPOPHE?t=70
I'm trying to follow this video having never used Blender to model something before, and at 1:12, he selects 3 vertices and drags them to the upper left. The rest of the object stays the same. When I try to do it, every other vertex moves, to a lesser extent. After some googling, I can tell you it isn't 'proportional editing'. I can find that option and see that it's not on and if I do turn it on, the other vertices move noticeably more. This is what my scene looks like before and after the transformation.



This is a cube with a Subdivision Surface modifier. I have Blender v2.82.7

I hope the info I've given is helpful, please let me know if you want pictures or info from another tab. Be explicit about how to find it, because I don't know what anything is.
The reason you're seeing that effect is that you have the 'On Cage' option selected for your subdivision surface modifier.



What this option effectively does it it allows you to work on the result of the subdivision surface on your mesh in edit mode, as opposed to the mesh before the subdivision surface.

Since the subdivision surface moves vertices based upon the positions of their surrounding vertices, when you move a vertex with 'On Cage' active, you also move surrounding vertices.

Simply toggle off the indicated button, and you should see the wireframe of your cube in Edit mode, and be able to move one vertex at a time again.