A lot of people have used Gmail for years and still don't know about Advanced Search!

Why is Advanced Search so important? Imagine you're searching for a message from your professor, Josiah. If you just type Josiah in the search box, you will get those messages...but you will also get the emails you sent him, emails on which he was CCed, emails where his name was simply mentioned, and even emails with attachments in which his name happens to appear. All this clutter will make it difficult to find the messages FROM him.

You can find Advanced Search by clicking the small arrow in the inner right corner of the search box:

This displays the advanced search options: 

Once you master advanced search, you might also be interested to know that you can create filters based on searches and type search operators in the search box without opening the Advanced Search screen.