Although simple searches can get you pretty far, you can perform more sophisticated searches if you know a few tips:

If you choose All as the scope for a search, Mail defaults to All next time too. If you search in a single mailbox, Mail defaults to searching the selected mailbox next time.

To search for a phrase, put it in quotation marks. A search for "apple pie" will find that entire phrase, but not messages with just "apple" or "pie" independently.

When you search in headers (To, From, Subject, Date), Mail matches the strings you type anywhere in a word. For example, a search for cat matches "bobcat" as well as "catch." However, when you search message contents using the Entire Message option, Mail matches only the beginnings of words--cat matches "catch" but not "scat." This applies to multiple words, too: In a header, press ring will match a message whose subject is "exploring impressionism" whereas a search of message contents would only match if the message contains words beginning with both "press" and "ring."