The Gmail Search Guide is a useful little post from the official Gmail blog which gives some valuable hints on how to search your message archives effectively. Most useful tip? Use the ‘show search options’ link to the right of the search box. Worth a bookmark if you’re an email junkie.
If remembering operators isn’t really your thing, that’s ok. There’s a “Show search options” link to the right of the search bar at the top of your inbox. Clicking that provides you with text fields you can fill in to get the precision of advanced search. Start there, but after a while you’ll probably find that using operators is a lot faster.