Some of these commands may be different for you because Moom allows you to change the shortcuts. The spirit is the same.
Ctrl+Shift+m activates the primary Moom menu (this is user defined).
There are several built in commands that can be swapped for the keyboard shortcuts in the preferences menu. The most basic shortcuts just involve nudging the window around with the arrow keys. There are user settings to define modifier keys for the arrows to enable additional controls.
The custom window sizes can also be assigned to keyboard shortcuts available when Moom is active. For example, I have two commonly used windows sizes assigned for quick access in Moom.
If you enable the "Repeat to Show Grid" option in the preferences, you get even more keyboard control over windows. In my case, I hit ctrl+shift+m+m and then choose the layout with the arrow and shift keys. The shift key allows multiple columns and rows to be selected.
Moom has excellent mouse controls but the keyboard commands make moving around the display look like magic. Combining the default OS X shortcuts like ⌘+Opt+H to hide all other windows with a good window manager like Moom, BetterSnapTool or BetterTouchTool makes a huge difference in the way I work.