How to check if a player has already touched something once?

Is there a way to check if a player has touched something once and then shut it down for only that player?

Like kingdom5 said, you could do this by creating a dictionary of people who have touched the part, to recognize if the player has touched it before. This would basically just act as a one-way debounce method for each player. Here's an example:

-- Players service
local players = game:GetService("Players")

-- dictionary of people who touched the part
local touched = {}

-- Assuming the script is inside a part, the following
-- applies.
script.Parent.Touched:connect(function(hit)
	-- Get the player from the character
	local user = players:GetPlayerFromCharacter(hit.Parent)

	-- If the player exists, then...
	if user then

		-- Check to see if the user exists in the dictionary
		if touched[user] then
			print("Player has already touched this part")
			return -- If it does, return to discontinue.
		else
			-- If the player doesn't exist in the table, then
			-- touched[user] = true adds them.
			print("Player has touched the part for the first time")
			touched[user] = true
		end

		-- This will only fire once per player, due to our
		-- return instruction if the player exists in the table
		print("Part was touched")

	end
end)

Hope that helped, let me know if you have any questions.