Drum Tuning Basics
Clear out any dust/drumstick fragments/other stuff when you take the drumhead off.
Tune the batter drumhead first, so stop the resonant head from interfering: Rest it on the drum stool.
Put the drumhead on and make sure it is seated. Press in the center and around the edge to make sure it fits snug against the bearing edge. If not, you'll have a very hard time tuning your drum. Don't worry if the head makes cracking noises, this is normal.
Put on the hoop, and insert the tuning rods into each lug.
Finger-tighten each rod (screw it as tight as you can with only your fingers). Double-check the ones you've already done (they can usually be tightened more)... This ensures each rod starts with the same amount of tension.
Tighten each lug a 1/2 turn with a drum key. Following the pattern in the diagram below, always tighten the opposite lug from the one you've just turned (don't tighten two lugs side-by-side unless you're looking for a specific sound).
Listen to the drum as you're tuning it.
Continue to tighten each lug, 1/2 turns if you're still far from your desired sound, otherwise 1/4 or 1/8 turns as you get closer to the pitch you want.
Experiment - if you're unsure of what sound you want, listen to what your drum can do.
Find out how it sounds at low, medium and high tuning.
Check the pitch of each lug once you're close to the sound you want. Dampen the center of the drumhead with your finger and lightly tap the head a few inches in from each lug (with the drum key) - some of them will be higher/lower in pitch. Mismatched lug tunings will give strange overtones. Do small tuning adjustments to minimise this (and if there's one lug pitch you prefer, tune the rest of them to match). You'll usually need to tune the opposite lug the same amount: usually two opposite lugs will share the same pitch (the drumhead is stretched equally between them). This part can be difficult and takes time to master. If you're struggling here, try the Tune-bot.
Repeat for the resonant head. You can tune the resonant head to the exact same pitch as the batter head to achieve the most sustain, or higher/lower than the batter head. This is completely down to personal preference - try out different options and listen to how the drum responds.
Drum tuning takes practice
Don't stress if you find yourself completely detuning the drum to start again (this is often better than trying to "fix" a severely out of tune drumhead).
Done all of the above and still struggling to tune your drums?
If you're new to drumming it can be frustrating when you just want to play and have a good sounding kit. Spend time learning to tune your drum kit, but also make sure you spend time having fun and actually playing.
There are a few options to quickly eliminate strange ringing and overtones, tune your drums more accurately, or control your sound, giving you more time actually playing.
Some drumheads are just easier to tune.
Try thicker drumheads with some form of sound control like the Evans Hydraulic, Remo Pinstripe, Evans EC2S, or the Aquarian Super 2 with Studio X-Ring. These drumheads are more controlled, warmer, and more durable, but they lack sensitivity and character (especially at lower volumes).
Dampening and sound control accessories can help reduce strange drum ringing and eliminate unwanted overtones. Moongels are incredibly popular for this, and there are also o-rings, bass drum mufflers, and more extreme sound changers like the Big Fat Snare Drum. Just don't overdo it, and try to use these things to complement your sound rather than covering up for poor drum tuning.
Check the bearing edges of your drums.
If your bearing edges are damaged, you'll have a very hard time tuning your drum set no matter what you do. Before putting a new drumhead on, take a look around the bearing edge (where the drumhead makes contact with the drum shell). Tiny bumps or dips here may affect the sound a little, and you will have big tuning problems if there are large areas where the drumhead can't make contact with the drum shell. Get the bearing edges re-cut by a professional if needed.
See the Drum Sound FAQ
to learn about the factors influencing your drum sound.
Knowing exactly how things combine to influence your sound will help you figure out what you need to target to get the sound you want.
The best thing you can do is experiment
Crank your drumhead all the way up to see how far it can go before you completely lose the sustain, and all the way down to see how low it can go.
Try out different batter and resonant head tuning combinations.
Think about how the different drumhead variables influence your sound.
Spend time to get it right.