First time to China! have a layover in Beijing

Hi Im a U.S citizen with a passport and I'm going to Korea and have a layover in Beijing. On my transit back to the USA I have a 19hr 30min layover as well and I would like to stay the night in Beijing. Is there anything I should do prior to my flight to request a 72 hr visa free transit? Also how do I get my luggage? I don't know Chinese and I'm traveling alone so I'm just worried about loosing my luggage and having difficulties getting transit access. Also Im going to be arriving around 7pm so is there anything to do in the evening or something in the morning before my 3pm flight? Thank you!