I would like to know if there are any tips on tuning drumheads; I keep hearing harmonics.
Dave Weckl has a great video for tuning drums
In response to your harmonic problem.
I'v always found it handy to look at the top and bottom heads of the drum as providing 2 different functions. Tune the top head, so that its tight enough to get a nice rebound from your stick and try to make sure that the drum ring is evenly placed on the drum. While tuning you might want to look at the drum from its side to make sure its even.
Now use the bottom to fine tune the sound of your drum. The tighter the bottom the higher-pitched it gets. That should get rid of your harmonics or help you find it and tune it out. If your still getting a slight ring then listen to which head its coming from. Once you find the ringing head then its usually 2 tuner bolts that are right next to each other that are too tight. You need to re-balance the tuner bolts by loosening and tightening them. Play around with it until the ring goes away.
I can't believe nobody has mentioned the Drum Tuning Bible yet.
The best way I found to tune drums is a technique that I have appropriated from many years of watching others, videos, etc. It involves adjusting one lug to the pitch you want (eg, relative low or high, depending on which tome/drum it is) and then matching each additional lug to that by going around the drum. It takes practice, but I have found it to be a great method.
I have also met others who actually use a tuner to get the exact frequency they want on a section of the head, and then use a round-about or criss-cross pattern to tune. I prefer my method but both seem to have merit.
Regarding top and bottom heads. I usually start with tuning them the same. If this is good for general playing, I leave it alone. If I need something different for the tune or piece, I change. For instance, my snare typically runs a very tight diplomat because I want that pop. I can't stand the round, loose sound of a snare drum. I like tight, piccolo sounds with a deep-dish girth.
The thing with technique from pros, etc, like Dave Weckl (who, I should add, is in my top three favorite drummer list) is that you end up modifying it as you go anyway. So these instructional viedos are good for hints, and tips, but in the end, you are going to develop your own method.
A tip for getting the levels right on your toms and snare is tune the top and bottom drums to the same pitch and use the stick to tap adjacent to each of the tuning keys individually, if they have the same tone near each tuning key the drum will be tuned evenly and will make the drum sound a lot cleaner.