I have a US passport. How do I get the 144hr visa when I visit Beijing?

If you transit country A-Beijing (144 hours)-country B, you will be able to use the 144 hour free transit in Beijing. When you board the flight in country A, you need to inform the carrier that you want to use the 144 hour free transit in Beijing. After arriving in Beijing, you can go to the transit counter to apply for the 144 hour free transit.

So when I get on my flight from the US and arrive in PEK(Beijing), you're saying I need to inform them that I want to get the 144hr visa, correct?

You should inform the airlines when you board the plane in US.

Thank you that is very helpful.