How to detect when player enters game?

game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(character)
        script.Parent.BackgroundTransparency = 0.1
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.2
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.3
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.4
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.5
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.6
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.7
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.8
        wait(0.1)
        script.Parent.BackgroundTransparency = 0.9
        wait(0.1)
        script.Parent:Remove()
    end)
end)

That should work.

game.Players.PlayerAdded

This fires when a player joins the game.

EDIT: Nvm, just realised you wanted UI to be transparent, sorry.

First, you will have to put a script in Workspace.

Put this code in the script:

local Players = game:GetService("Players")

Players.PlayerAdded:Connect(function(player)
    wait() --DO NO REMOVE THIS WAIT
local UIElement = player.PlayerGui.ScreenGui.Frame.TextLabel --player.PlayerGui is game.StarterGui
UIElement.BackgroundTransparency = 0.1
wait(0.1)
UIElement.BackgroundTransparency = 0.2
wait(0.1)
UIElement.BackgroundTransparency = 0.3
wait(0.1)
UIElement.BackgroundTransparency = 0.4
wait(0.1)
UIElement.BackgroundTransparency = 0.5
wait(0.1)
UIElement.BackgroundTransparency = 0.6
wait(0.1)
UIElement.BackgroundTransparency = 0.7
wait(0.1)
UIElement.BackgroundTransparency = 0.8
wait(0.1)
UIElement.BackgroundTransparency = 0.9
wait(0.1)
UIElement:Remove()
end)

Find player.PlayerGui.ScreenGui.UIElement

Change UIElement to the name of the UIElement in your ScreenGui Do not change player.PlayerGui, player.PlayerGui is game.StarterGui. Using game.StarterGui will not work.

If you have any questions reply to this answer.

Change your Script to a LocalScript. Changing this should allow you to detect when players join and when you should change the Background Transparency of the GUI.

Because you didn't outline what the purpose of the script is, I'll assume that PlayerAdded is the best way to do whatever you're doing.

Your code can also be shortened using loops like so:

players = game:GetService("Players")

players.PlayerAdded:Connect(function(player) 
    player.CharacterAdded:Connect(function(character) 
        for i  = 1, 10 do
            script.Parent.BackgroundTransparency = i/10
        end 
    end)
    script.Parent:Destroy()
end)

If I am wrong about the intentions of your code please leave a comment and I can find a solution :)

Okay, this site should help. You're looking for PlayerAdded. You can (optionally!) use it with CharacterAdded, which is actually kind of also a function of PlayerAdded.

game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(character)
        --code
    end)
end)

Also, it's really not very good to repeat code instead of using loops.

for i = 1,10 do
    --code
end

Change your script to a LocalScript instead, too. Your code should look like this (if you changed it to a localscript):

local textbox = game.Players.LocalPlayer.PlayerGui.ScreenGui.TextBox
for i = 1,10 do
    textbox.Transparency = textbox.Transparency +.1
end