Find an old message
Search inside Messages, and the timeline that shows everything with one person.
Search your conversations
The search field at the top of the Messages tab filters your conversation list as you type. If nothing matches, Kool says so with the words you searched for.
Search inside a thread
Message search looks through the text of your messages, so a distinctive word from the message you remember is usually enough.
The timeline
Open a conversation, tap the header, then tap Timeline. This is the whole relationship in one scroll: messages, calls and email with that person, in order. Filter it with Everything, or narrow to one kind of item. Calls show their length, missed calls are marked, and email sits alongside the rest.