Open up Garry's Mod and go to Options.
Go to the Keyboard tab and click the "Advanced..." button. A new window will pop up that looks like this:
Check "Enable developer console (~)" and click OK to close the window. Click OK to close the Options window.
Press (~), it's below the ESC button, to open up the console.
Type into the console:
bind YOURKEYHERE +HATMenu
Use any key you like, I personally like the 'x' key. Press enter after you're done. You can close the console if you'd like, I'm not stopping you.
When you start a singleplayer or multiplayer game using HAT, you can now press the 'x' key, or any key you set yourself, and the HAT menu will appear. Let go of that key and it will disappear.
Now that you've hopefully correctly setted up HAT, why not use it? Click here to learn how to animate with HAT