Here's a quick reference for all the main controls we went over:
Alt + W --- Maximise Viewport Toggle. This switches between the screen being divided into 4 or just 1.
Scroll Mouse Wheel --- Zoom in and out.
Click & Drag Mouse Wheel --- "strafe" the viewport, drags the screen around.
Alt + Click & Drag Mouse Wheel --- pan around whatever the viewport is focused on.
P --- returns your viewport to the "perspective" view if stuff starts to look weird.
Z --- focuses the viewport on the currently selected object. If nothing is selected, it'll just zoom so that everything in the scene is in view.
There are a ton of other hotkeys, most of which are helpfully listed here!
The button on the left showing the mouse clicking a cube is the SELECT tool (you can also press Q). This is the default you start off with and you can't do anything with it except select stuff (obviously). This is useful if you want to select stuff without moving it slightly by accident (which can happen if you're in the MOVE mode).