Basically I want to make an elevator that has buttons and when you click them you get teleported up a floor or down a floor.
Use the Model:MoveTo(Vector3) function for that. It teleports the specified model (in this case the player's character) to the specified Vector3.
Connect to the ClickDetector's MouseClick event to detect the click.
Update:
Insert a ClickDetector into the part that is clicked. Insert the following Script into the ClickDetector:
script.Parent.MouseClick:Connect(function(plr) plr.Character:MoveTo(Vector3.new(X, Y, Z)) end)
For X, Y and Z add the coordinates the player should be teleported to.