How would I make this so only one player would see this?

Well, you could approach this a few ways. You could have some RemoteEvents set up, but that'll take more explaining to do. The simple way to do it, is to compare the person who touched it's name, and the LocalPlayer's Name: (LocalScript)

game.Workspace.Portal1.Touched:connect(function(hit)
	if not game.Players:GetPlayerFromCharacter(hit.Parent) or game.Players:GetPlayerFromCharacter(hit.Parent).Name ~= game.Players.LocalPlayer.Name then return end
	script.Parent.Parent.Menumusic.Menu:Play()
	script.Parent.Parent.Background:TweenPosition(UDim2.new(-0.1, 0,0, 0), "Out", "Quad",2)
	wait(2)
	script.Parent.Parent.RED:TweenPosition(UDim2.new(0.02, 0,0, 0), "Out", "Quad",2)
	wait(1)
	script.Parent.Parent.Buttons.Frame.Telport4:TweenPosition(UDim2.new(0.1, 0,0.94, 0),"Out", "Quad",2)
	wait(1)
	script.Parent.Parent.Buttons.Frame.Telport3:TweenPosition(UDim2.new(0.1, 0,0.74, 0),"Out", "Quad",2)
	wait(1)
	script.Parent.Parent.Buttons.Frame.Telport2:TweenPosition(UDim2.new(0.1, 0,0.54, 0),"Out", "Quad",2)
wait(1)
	script.Parent.Parent.Buttons.Frame.Telport1:TweenPosition(UDim2.new(00.1, 0,0.34, 0),"Out", "Quad",2)
	wait(0.1)
	script.Parent.Parent.Buttons.Frame.Back:TweenPosition(UDim2.new(00.1, 0,0.24, 0),"Out", "Quad",2)
end)