How do I make a gui fade in when a player dies?

Nice try, you did get almost everything right, but the reason this is not working is maybe because you were refering to game.Players.LocalPlayer in a server script (a normal script) which you can't do. You have to do it in a loca script, that also applies for GUIs, I'm assuming this server script is parented to a UI (script.Parent), which won't work out as well, UIs need to be controlled from a local script, because they are local or in other words client-sided, meaning they are handled from the player's computer (also known as the client) and not the server. So change this to a local script, and another thing to point out is, this part

    script.Parent.ImageTransparency = 1
    wait(0.1)
    script.Parent.ImageTransparency = 0.9
    wait(0.1)
    script.Parent.ImageTransparency = 0.8
    wait(0.1)
    script.Parent.ImageTransparency = 0.7
    wait(0.1)
    script.Parent.ImageTransparency = 0.6
    wait(0.1)
    script.Parent.ImageTransparency = 0.5
    wait(0.1)
    script.Parent.ImageTransparency = 0.4
    wait(0.1)
    script.Parent.ImageTransparency = 0.3
    wait(0.1)
    script.Parent.ImageTransparency = 0.2
    wait(0.1)
    script.Parent.ImageTransparency = 0.1
    wait(0.1)
    script.Parent.ImageTransparency = 0
    wait(0.1)

Logically speaking, it should work as you'd think it would, but there is a much more efficient way to do it that offers more readability, using for loops. For loops are basically loops that loop a certain amount of times.

for i = 0, 10, 1 do
    print(i)
end

This loop will loop from 0 to 10, going up by 1 each loop. i is the value the loop is currently at. So it would print 0 1 2 3 4 5 6 7 8 9 10.

for i = 0, 14, 2 do
    print(i)
end

This would go from 0 to 14 going up by 2, so it would technically loop 7 times.

We can utilise this, we can go from 0 (invisible) to 1 (visible), by 0.1 for example so it does it slowly, and we set the transparency value to i, because represents the value that we are making go from 0 to 1. Think a bit about what we did, it's pretty cool.

game.Players.LocalPlayer.Character:WaitForChild('Humanoid').Died:connect(function()
   for i = 0, 1, 0.1 do
    wait(0.1) --we add a wait so it doesn't finish the loop instanly
    script.Parent.Transparency = i
  end
end)

And just in case you are wondering what :WaitForChild() is, it basically waits for an object to load, in this case if humanoid didn't load yet it would wait for it.

here try this:

game.Players.LocalPlayer.Character:WaitForChild('Humanoid').HealthChanged:Connect(function(health)
    if health <= 0 then
        script.Parent.Visible = true
        script.Parent.ImageTransparency =  0
        for i  =1,10 do
            script.Parent.ImageTransparency =  script.Parent.ImageTransparency -0.1
            wait(0.1)
        end
    end
end)

tell me if theres any errors still and ill help out