Most controls are intuitive and/or covered by the tutorial, but there are a couple quirks to make note of. Note that all modifiers (Shift, Ctrl, Alt, etc.) can be freely combined, except where otherwise stated.
One particularly useful shortcut the manual lacks is:
Ctrl + Z: Select all units of the selected type(s) on the map. For example, if bombers are group 4, pressing 4, Ctrl+Z, Ctrl+4 at any time will make sure all your bombers are in group 4 so they can strike when the time is right. You could also zoom out, double-click a bomber, and Ctrl+4.