See the man page or right click terminator -> Settings.
The config file can be found in
F11 Toggle fullscreen
Ctrl + Shift+ O Split terminals horizontally
Ctrl + Shift+ E Split terminals vertically
Ctrl + Shift+ W Close current Panel
Ctrl + Shift+ T Open new tab
Alt + ↑ Move to the terminal above the current one
Alt + ↓ Move to the terminal below the current one
Alt + ← Move to the terminal left of the current one
Alt + → Move to the terminal right of the current one
Drag and Drop
The layout can be modified by moving terminals with Drag and Drop.
More key commands
Terminator also supports plugins. Please read Writing Terminator plugins for more details.