How would I format the end of a function like this?

Your problem may be that Value may not be existant at the time of the code executing, consider using the WaitForChild method, for the WaitForChild method will repeat waiting until the Child is existant, and will return it when so, also, let's add an Identifier to your code so that you don't have to keep using game.Players.LocalPlayer.Value over and over again, to make it a bit more efficient, now, let's fix up your code;

repeat wait() until game.Players.LocalPlayer --This will repeat waiting until 'LocalPlayer' is existant, LocalPlayer is the Player the LocalScript is running for, as said on the WIKI
local Value = game.Players.LocalPlayer:WaitForChild("Value") --This will repeat waiting until 'Value' is existant within the Player, and will return it, once it exists, identifier 'Value' will, well, identify it

function change() --This is your original function
if Value and Value:IsA("StringValue") then --I am assuming this is a 'StringValue' type instance; The 'if then end' statement will check the conditions for a block of code; This will check to see if 'Value' is existant, and 'Value' is a 'StringValue' type instance
print("Function 'change' fired! :D") --This will print if the conditions are/were met; This will print the string 'Function 'change' fired! :D' into the Output
end --This ends the code block for the 'if' statement
end --This ends the code block for the function

game.Players.LocalPlayer.Value.Changed:connect(change) --Now, whenever something has changed within 'Value' [Name, Parent, Value, ect.], the event '.Changed' will fire the function 'change'

Hope this helped, and Happy New Years!

Yes, your script would error due to the value being nil at some moments. But to get around this, we can make a sort of custom changed function.

We can do this by setting an 'oldVal' variable. Then having a While loop, followed by the checking of IF the value is nil. If it isn't nil then we continue with the script to compare the 'oldVal' with the currentVal. Then if there's a change we can put some code in(:

Somthing like this:

local val = game.Players.LocalPlayer:FindFirstChild("ValueName")
local oldVal = 0

while wait(1) do --to reduce lag, have a 1 second interval.
    if val then
        if oldVal ~= val.Value then
            oldVal = val.Value
            --Your Code--
        end
    end
end