How to script a click function that changes a text, using type writer?

If you want to make a function that types one letter at a time, you just make a new function that makes a copy of the original string (so that it doesn't override it) and then you use the string:sub() method to make it extract a portion of the string and then you do this with a for loop.

Consider the following code:

local text = "Hello World";
print(text:sub(1,5)) --> Hello

That codes prints the 5 first characters of the string ("Hello").

Now, you just need to make a numeric for loop that goes through each character and updates the TextLabel:

function writeText(text, textLabel)
    for current = 0, #text, 1 do
        textLabel.Text = text:sub(1,current)
    end
end

writeText("Hello World", script.Parent.TextLabel)

There you go.

Hello, utrabem!

I made some changes on your script, first of all, :Connect(function() is a function, so you don't need to call another function, to get a string lenght, use string.len() and if you want the letters to change on the string, use str = str2!

local noob = "Okay, here's our menu!"

script.Parent.MouseButton1Click:Connect(function()
    for a=1, string.len(noob)+1 do 
        script.Parent.Text = noob
        noob = string.sub(noob, 2)
        wait(0.06)
    end 
end)

Attention, I didn't made any changes on what your script does, this makes the words be REMOVED like somone writing...

Helpful links:

Roblox Dev - Lua Libraries - Strings

Good Luck with your games