> how does selling the shirts work?
Create design, upload to Amazon, sales show up under analyze tab, once per month they pay you for previous month sales. Be sure to read over the resource pages, https://merch.amazon.com/resource.
> Do I have to advertise to sell them?
No, organic traffic already on Amazon is what many utilize. Buyers find you by the listing text, utilizing relevant keywords and phrases that will help buyers find your shirt is key.