My question is, how would one make an event call trigger when the player presses a key, say, "H"?
An example: Player press "H" to call an event, $scene = Scene_Open_Menu.new
isn't there an event option for button input?
Conditional Branch: Button Pressed
Also, Button Input Processing: Conditional Branch: Variable
They can each be used for different situations. Regardless, you will probably want a parallel process common event to do it.
that's only useful if you want to use the predefined buttons. I have no idea if H is one.
There's a script somewhere around for button input. Have a bit of a search in the scripts database - I'm almost certain I got it from here.