On Amethyst, you're going to access the relay menu by clicking the sparkly icon on the top right.

In order to "save" the relays you've added to the list, you need to "post" to all of them. Do not overuse the "post" button too liberally, or you will be marked as spam and banned from all the relays.

I am also new to Nostr, and I'm only half confident with this information, so I do encourage personal research.