How to put cooldown on a button?

This method in general is usually called a debounce.

The basic idea is that you keep track of some state of whether or not its enabled.

Whenever the event happens (like pressing the button) you mark it as disabled. After the time is up, you re-enable it.

That will end up looking something like this:

coolingDown = false

function event()
    if not coolingDown then
        -- Do whatever else
        -- Do whatever else
        --
        coolingDown = true
        wait(10)
        coolingDown = false
    end
end

-- calls / connections to `event`