Place the drum on a carpeted floor or a drum throne. It's nice to have the opposite head muffled while tuning.
Assuming you have seated you new heads, proceed:
Do the following steps 1 and 2 to both top and bottom heads, one at a time.
1- Loosen head almost all the way, not quite so loose that tension rod washers lose contact with the rim, just enough to put some slack into it. The head must stay centered on the bearing edge, where it was seated, so don't loosen too far. The head can get plenty of slack without coming loose from the drum, if that makes any sense.
2- Getting the Slack Out
Why did we just put slack into the head if we're going to take it out again? We are trying to find the lowest possible tension at which the head will produce a nice tone, and that's an easy way to start. Continue...
Choose a starter rod (as you did in the seating process). Slightly tighten each rod-- one at a time, (using the tensioning pattern is a good idea) in the following way. Tighten about a quarter to half turn. While turning the rod, use a stick or finger and tap the head about an inch in from the rod you are turning. Listen to the sound it makes. It will be all floppy at first until you reach a point where the head gets the slightest bit of tension and produces an actual tone with a little resonance. Do this with each lug just to the point where there is only an eighth to quarter-turn difference between a "floppy" sound and "a tone with a little resonance." This should take very little time, unless you loosened the head too far in step 1.
This should be the lowest tension that the drum will produce a drum-like sound.
[You should have done Steps 1 and 2 to both the top and bottom heads.]
3- Getting Even Tension on the Head
After step two, you should have a very open boingy, maybe oscillating, sound-- boow-anga-wanga-wanga. This is not a very usable sound. Now tighten each lug of the batter head just slightly-- about one sixteenth of a turn (like from 9 o'clock to 10 o'clock-- I know, that's one twelfth, but you get the point.) Hit it again and listen. It probably cleaned up the sound tremendously. Maybe not. If step 2 was done very accurately, the head should have very even tension, already. But, this isn't always the case.
You should make sure the head has even tension at each lug. Just tap around the outside of the head, next to the rim by each lug, and listen for obvious high or low notes and correct them. Use a stick or your finger. You can actually just touch the head and you will hear a pitch. Do what works for you.
Loosen the lugs that are high and tighten the low ones.
Now, to throw a wrench in the works. You always should tune "up." When a lug is loosened, the head may not always slip back from the bearing edge. Sometime they bind slightly. To avoid this, you should always loosen more than you need to and then tighten back. For example, if you need to tighten an eighth of a turn, loosen an eighth of a turn and then tighten back up an quarter. I think this is done with guitar strings, too.
Slightly tighten the low lugs and slightly loosen the high ones, until they are close to the same pitch. Even it all out, but don't get too anal about it. You will never get them all to match perfectly. The physical properties of the whole drum thing just don't make it probable. It's not really that necessary, either. Just listen for obvious or gross differences and get them close. The head should now be evenly tuned, or in tune with itself. The head has even tension at all points-- or pretty darn close.
At this point, the drum will still sound pretty low, since you've only tightened it slightly above the "floppy" stage, and evened out the tension, right? It may still sound warbley, just like at the beginning of this step. Now that you have even tension, you just need to make the same adjustment at each lug to raise or lower the pitch of the drum. Very slight adjustments, again, even just one sixteenth of a turn, will make a big change in the pitch. A very slight tightening of each lug will clean up a warbley sound. Before choosing a pitch at which to tune the head go to step 4 to learn how the individual tensions of the top and bottom heads affects the sound of a drum.
4- Adjust relative tension.
The relative tensions of the top and bottom heads is what controls the resonance of a drum. Usually, you tune the top head to the general pitch you want the drum. Then you tune the bottom head to produce the desired resonance.
There are three ways to set the relative tension of the heads and each affects the resonance differently.
A. Top and bottom heads are the same . This will usually produce the most sustain, or resonance. It also gives the drum the most pure tone or pitch. This depends on the depth of the shell. Some times you will need to go slightly tighter with the bottom head to have this result. Speaking of tighter...
B. Bottom tighter than the top . Depending on the depth of the shell, this may increase the resonance if it is slight. But as it gets tighter, it will start to choke the sustain.
C. Bottom head lower than the top. Less sustain the looser it gets. Again, going to an extreme will choke the drum.
In B and C, there is a difference in the relative tension of the heads. Anytime you tune this way, you can get 'pitch bend' in the sound of the drum. This is just another option in sound, it is either good or bad, depending on your preference. However, pitch bend will only occur at lower tuning ranges.
To hear the relative tension of the heads, strike the batter head and then the bottom head separately to hear the tone of each. Sometimes it's difficult to hear the difference because you are hearing all the overtones of the drum. You may need to put your hand on the other head to dampen it so you can hear more clearly.
It only takes a slight adjustment of all tuning rods to change the relative tension of the heads. In fact the process of steps 3 and 4 is usually within a half turn of the drum key, once you get better at seating and evening the tension of a head.
5- Finding a tuning range.
This is totally a matter of personal taste. While there are no real rules in tuning there are some norms. In general, rock, funk, and blues drums are usually tuned in the lower ranges; often with some pitch bend that you can get down low; sometimes thuddy and boomy. Traditional jazz, however, is about opposite-- higher ranges with clean, defined tones.
Each drum will have a certain range of it's own of where it can be tuned-- how low and how high. This is often directly affected by the quality of a drum. Don't expect to have an incredibly vast tuning range from a $700 set of drums. But, don't ever think you can't get them to sound great, regardless. Even today's cheap drums will have a decent range in which to tune.
It's easy to run through the tuning range of a drum. You already found the low end, when you completed step 3. It's the point where the drum goes from sounding all floppy and warbley, to where it just starts to sing a little and sustain without warbles. All you have to do, now, is increase the batter head tension, slightly. This, of course will raise the pitch of the drum. Depending on where the relative tension of the bottom head is, the drum will either sustain longer or shorter. You either brought the batter head up to the same tension as the bottom head or you took it up higher. Now, make the same increase on the bottom head. The drum should sound much higher in pitch.
This is a delicate game. Often, it takes only minute turns at each lug, or even every other lug, to change the pitch of a drum. As you bring up the pitch of both heads, in unison, you will move up through the tuning range of that drum. Minor tweaking of relative tension will be necessary to keep good resonance. At some point, you will reach the highest end of the tuning range and the drum will start to "choke." No adjustments in relative tension will fix it. That is the end of the tuning range of that drum.
6- Tuning the drums to each other.
Again, there are no rules. If you are familiar with keyed instruments and like to tune to specific notes, you can do so. Some like to tune toms at 4th or 5th intervals, for example. Some just play it buy ear or have a certain song melody they tune to. Some tune each drum to the same area of tuning range, i.e.: lowest, or just below highest, etc. That way there will be a natural interval between the drums, if they have big enough changes in size (diameter).
When starting out, tune each drum to the same area of the tuning range, like just slightly above the lowest. See how they sound together, here. If you have the standard 12, 13, 16 inch toms that come with most kits, you will probably notice a much bigger difference between the middle and floor tom, than between the two mounted toms. It's obviously because of the jump in size difference-- three inches as opposed to one. If your middle tom is producing a nice tone, then just take the high and low toms up a little bit. This will put the low tom closer to the middle and the high tom farther from the middle. Whatever you need to do with changing the pitch of the drum, just don't forget to adjust the bottom head along with the top.
Also, you can use the bottom head to change the pitch of the drum slightly, without losing resonance. This is the fun (and sometimes frustrating) part of tuning. Just experiment and practice different tunings. If you totally mess up the sound of the drum, just go back to the beginning-- loosen the heads all the way and start over. As with drumming, you will get better with practice.