I created a script that works in studio but does not work in a normal game, help?

You are trying to index the local player through a server-side script. To fix this, you can use a feature of game.Players called "GetPlayerFromCharacter".

I'd also recommend using "local" variables.

local Anvil = game.Workspace.Anvil

local function Click(player)
    if player.Parent:FindFirstChild("Humanoid") then
        local player = game.Players:GetPlayerFromCharacter(player.Parent)
        local playerGui = player:WaitForChild("PlayerGui")
        local Gui = PlayerGui:WaitForChild("CraftGui")
        Gui.Enabled = true
    end
end

Anvil.Touched:connect(Click)

The first problem is that you cannot use LocalPlayer in a scipt, it only works in a local script as this type of script only runs on the players device so it knows who the player is. A script however runs on the server and is not linked to any player so there is no such thing as a local player to a script.

In my opinion it would be best to use a local script to show the gui but you can also use a server script.

Local script example in StarterPlayerScripts:-

-- we need something about the local player that we can check as this event will fire for all thing / other player that touch the anvil
local plr = game:GetService('Players').LocalPlayer

-- wait for a child called Anvil as the player will be downloading the workspace and it will take a small amount of time for it to be loaded
workspace:WaitForChild('Anvil').Touched:Connect(function(hit)
    -- check the player ie their name, there are other methods of checking the player this is just an example
    if hit.Parent.Name == plrName.Name then

        -- find the players gui and enable the gui

        -- we should use FindFirstChild instead of WaitForChild in case the player does not have the gui causing the function to wait infinity  
        local gui = plr:WaitForChild('PlayerGui'):FindFirstChild('CraftGui')

        if gui then -- if we have the gui then enable it
            gui.Enabled = true
        end
    end
end)

We can also use a server script to do the same task but we need to find the player first. we can use GetPlayerFromCharacter to return the player from its character model or nil if no player is found.

Script example:-

workspace.Anvil.Touched:Connect(function(hit)
    local plr = game.Players:GetPlayerFromCharacter(hit.Parent) -- the parent being the players model

    if plr then -- if we have a player
        -- follow the same process in the above script
        local gui = plr:WaitForChild('PlayerGui'):FindFirstChild('CraftGui')

        if gui then -- if we have the gui then enable it
            gui.Enabled = true
        end
    end
end)

Notes

Your script will run each time the event is fired with no delay / cooldown. I would recommend that you include a Debounce.

As this is safe to do on the client side and it would take a small amount of time to replicate the change from the server to the client I would recommend that you use the local script version. It would also cut down on resources required on the server.