How would one find which direction the mouse is moving at a given time?

The easiest way to do this is like so,

-- This is in a LocalScript
wait();
local player = game.Players.LocalPlayer; -- Sets player to be the localplayer
local mouse = player:GetMouse(); -- Sets mouse as the players mouse

while player.Character:FindFirstChild("Humanoid").Health > 0 do -- Just a check to see if the player is alive
    print("Mouse X: "..mouse.X..", Y: "..mouse.Y); -- mouse.X and mouse.Y return the position on screen that the mouses cursor is pointing at
    wait(0.5); -- Just a wait so it's not constantly printing it out.
end;

This script will print out the mouses location on screen every half a second. Here is a link to the wiki article for the Mouse class. Hope this helps!