To move one of your archived chats back to the main Chat List, open Archived Chats > swipe left on the chat > tap Unarchive.
If you don't see the Archived Chats folder at the top of your Chat List, drag the screen down for it to show up. If you are using folders, switch to All Chats first.
Note: When an archived chat gets a notification, it will pop out of the folder and back into your chat list. Muted chats will always stay archived.
These demo videos show how unarchiving works on Android and iOS: