Replying, editing and tidying up conversations
Open a conversation in Messages to write in it. Enter sends, and Shift+Enter starts a new line. Text faces such as :) and <3 turn into emoji when you send them.
Replying and reacting
Point at a message, or tap it on a phone, to see what you can do with it.
The reply arrow quotes the message above your answer.
Add reaction puts an emoji under it. Press a reaction to add yours, and press it again to take it back.

Editing and deleting your own messages
The pencil puts a message back in the box as Editing message. Once you save it, it shows edited.
The bin asks you to confirm. Everyone then sees This message was deleted. in its place, and it cannot be undone.

There is no time limit on either. Deleting a message does not stop sharing a file that came with it: the article on sharing files explains how to remove one.
Finding something
Search conversations... above your list finds a conversation by name.
Search at the top of a conversation looks through its messages. Type at least two characters. Up to 20 matches are shown, newest first, with who sent each one and on what date.
Who has read what
Each conversation shows how many messages you have not read, and the total sits on the Messages icon. Opening a conversation marks it read. Nobody can see whether you have read their message: there are no read receipts. You can see when someone is typing.
Archiving and deleting conversations
Open the menu beside a conversation in your list on the Messages page.
Archive takes it out of your list. Archived Conversations, at the bottom of the list, shows the ones you have archived. Their unread messages no longer count on the Messages icon, and they stay archived when someone writes, although you still get emails about them. Unarchive brings one back.
Delete takes you out of the conversation. The other person keeps it, with everything in it. If you write to them again later, you start a new, empty conversation, which counts towards your three new conversations a week.

Deleting a group you own locks it for everyone. The article on group conversations explains why.
My Notes
My Notes sits at the top of your list. It is a conversation with only you in it, for drafts, links and files you want to keep to hand. Nobody else can be added, and it cannot be renamed, archived or deleted.
Emails about new messages
When someone writes, you get one email for that conversation. The next one comes only after you have read it, so a busy conversation never floods your inbox, and there is none while you have the conversation open on screen. You can turn these emails off under Settings → Notifications, in Messages.