This is tricky, because their user interface does a really dumb thing.
This article assumes you are setting up Podpage with your fill domain name (www.yourdomain.com). If you're setting up a subdomain (podcast.yourdomain.com), just replace www with podcast.
First, delete any and all records that start with www (or the subdomain you're using)
Then, add a new record at the bottom. Scroll down and find the ADD button
The natural thing would be type www (or your subdomain) first. But there's a really stupid bug: When you select CNAME, it deletes www (or your subdomain)!
So, make sure to re-add www (or your subdomain) after you choose CNAME.
Enter the Podpage DNS
Follow the instructions from this article to finish setup:
Then, hit save at the top of the screen
Scroll up to the top and in the left you'll see a SAVE button. Click that! I missed this the first time.
Hope this helps!