They get 30 days to pay. I used to start sending reminders if they were late by even a day past that, but I quickly learned that can unnecessarily embarrass or annoy some clients, so now everyone gets a two week grace period after the 30 days are up.
I send a gentle reminder just to my immediate point of contact to start. If that doesn't work, I start sending more business-like requests for payment every week, and I CC anyone I think might help make it happen.
I've never fired anyone, and everyone has eventually paid (knock wood), but there have been times when I assumed the money was a lost cause (though never five figures worth like the person who shared this blog post).
But more than once, I've had a client contact me and request new work, and I've had to remind them they still have an unpaid invoice. I'll tell them I can't start anything new until the old work is paid. They almost invariably blame the delay on their billing department, and the money eventually finds its way to me.