How would I shorten this?

A for loop. Go to this link for help on what they are.

This code will work:

for i=1,10 do
    script.Parent.BlackScreen.BackgroundTransparency = 0.1 * i
    wait(0.1)
end

You can use a numerical for loop like so:

local blackScreen = script.Parent.BlackScreen; -- Create a reference to the GUIObject
for i = 0.1, 1, 0.1 do -- Start at 0.1, finish at 1, increase i by 0.1 every iteration
    blackScreen.BackgroundTransparency = i; -- Se the property to whatever I equals
    wait(0.1);
end

By using a for loop to increase the transparency (Sorry if script didn't work);

for i = 1, 0, 0.1 do --Heres our four loop
script.Parent.BlackScreen.BackgroundTransparency = i --There is where 'i' will come in
wait(0.1) --Will wait each 0.10 milliseconds
end --The end to end the `for` loop code

Hope this helped!