The keyboard shortcuts are self explanatory, but the snap areas can use some explanation if you've never used them on Windows or other window management apps.
Drag a window to the edge of the screen. When the mouse cursor reaches the edge of the screen, you'll see a footprint that Rectangle will attempt to resize and move the window to when the click is released.
The preferences window is purposefully slim, but there's a lot that can be modified via Terminal. After executing a terminal command, restart the app as these values are loaded on application startup.
If you wish to change the default shortcuts after first launch click "Restore Default Shortcuts" in the settings tab of the preferences window. Alternatively you can set it with the following terminal command followed by app restart. True is for the recommended shortcuts, false is for Spectacle's.
There's an option in the preferences for Move to adjacent display on repeated left or right commands. If this setting is not checked, then each time you execute a half or quarter action, the width of the window will cycle through the following sizes: 1/2 -> 2/3 -> 1/3.