Hotkeys let you do use some buildings without mouse clicks - like pressing P to plane a board on a wood plane. Hotkeys are indicated on menus by a letter in square brackets at the end of an option, e.g. "Plane a piece of wood into a board [P]".
To use hotkeys, you need to enable an option to allow you to minimise your chats (otherwise keypresses go to chatting). Under the Utilities -> Options:Chat-Related, check the option "Chat and Inventory can be minimised". If you want to continue to monitor chat tabs, also check the option directly underneath, "Minimized chat-channels are still visible".
To use a hotkey on a building:
Hotkeys are especially useful for planing boards - cycle the mouse over an array of carpentry shops pressing P quickly to cut lots of boards quickly.