There's a Hearts tutorial at World of Card Games. It's designed to
introduce you to the mechanics of Hearts, but barely scratches the
surface when it comes to strategy. The help box has a few hints, too, but it's minimal.
After playing a few hundred games of Hearts, I think I've gotten a little better at it. This was, in part, due to some players who discussed strategy with me. Thanks to those who did so in a polite manner, you know who you are!
It's nice to share, so I wrote up a discussion of Hearts strategy and placed it on the site. There's a comment section where anyone can add their thoughts, and you can also tweet them, or post in the comments section here. Or send me an email. I will rewrite sections of that page based upon feedback.
I want to mention that I like the way that some more expert players try to help those who are beginners to the games. I don't mean the ones who mock beginners! I mean the ones who offer to explain or give a short tip to people who confess to being inexperienced. It benefits everyone to help those who are new. They are more likely to continue to play when people are friendly and not mean. It's a win-win to get more good players to your favorite card game.