I do not see anywhere to create a coupon code inside of the Abandoned Cart module itself. Do we create them under the marketing tab and just use one of those? Any detailed info on how to properly set this up would be appreciated. 

I've asked the same question. I'll post it here when support replies.

From support: 

The discount code is generated automatically when the email is being sent. However, if you want to use your own generated code, you have to replace the short-code {discount_code} in the mail template with your custom discount code.

Hello,

I believe this resolves your question so I will mark the issue as solved.

Enjoy the AbandonedCarts module!