How do renewals work? If I purchase say a theme at $20 and the renewal is $20 every year (just example numbers)... am I prompted in a year to make that payment? Is it automatically taken out of my PayPal? How do I get "out of" a renewal on something I found didn't work on my site and I no longer wanted to use it or renew?

It is up to you if you want to renew or not, no need to get out of renewal or anything.

Simply unfollow the file on marketplace  

What @TAMAN said.

Plus: you won't be able to download versions released after the purchase has expired.

On 1/23/2017 at 7:01 PM, Primus Palus said:

How do renewals work? If I purchase say a theme at $20 and the renewal is $20 every year (just example numbers)... am I prompted in a year to make that payment? Is it automatically taken out of my PayPal? How do I get "out of" a renewal on something I found didn't work on my site and I no longer wanted to use it or renew?

On all of your Marketplace purchases:

1. You can go to https://invisionpower.com/clients/purchases/ to manage your purchases.  
2. You will be sent an invoice 7 days before the expiration of the purchase, asking you to renew.  You will need to manually renew through PayPal.  (If you have account credit, then your account credit will be automatically applied.)  

You are never locked into a purchase, and you can always choose to cancel your purchase at any time you want.