I've tried to do this by myself and the wiki isn't much help either, does anyone else know?
Like this: GUI
This is a quick tutorial on how you do it: Firstly, you need to change the GUI's size property, which normally is defaulted to an offset of 200 and 50, to a UDim2 of {1,0},{1,0}. If you have ANY offset in your billboard GUI, this will have it resizing to fit to the player's screen. Secondly, you need to have all of its members in SCALE. Do not use offset at ALL!
Hope this helped, leave a comment if you did not understand.