Just a quick little question, in this video
At around 41:20 he someone makes it so he can edit the vertices on the circle, but he never says what button he hits to do it, and I've been googling and I can't find it.
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He's in edit mode, try pressing the Tab button to enter it.
By the way, I'd absolutely recommend you checking out this tutorial, especially the first 2-3 lessons. It goes in detail about Blender UI and all its menus and submenus.
If you're referring to what he does at 41:02 (not 41:20), just after adding a cìrcle, at the bottom of the toolbox panel (left to the 3d view, activate with T, there is a slider which is set at the default circle vertices count, but before exiting edit mode, you can edit it: he changes it to 200, in the video.