Sit down. It will be more comfortable and easier to drone for a longer period of time if you're sitting.

Relax. Get your mouth wet, your lips loose, and your breath coming easy. Have a drink ready, if you're a bit dry.
Hold the didgeridoo in front of you. Find a comfortable way to hold it steady. Some people like to hold the end of the instrument with their feet.
Choose your playing style. You can play the didgeridoo directly in front of your mouth, or off to the side of your lips. Each way has its own benefits, and one may be more comfortable to you.
Loosen your lips and blow through them like, "Brbrbrbrbrbrbr." If you are familiar with playing brass instruments, this will be something like getting ready to play a tuba.
Bring your lips to the mouthpiece to seal, but not too hard. You want to leave room for your lips to move a little.
Blow the same loose raspberry. You may make some ugly noises at first, but the didgeridoo will help you find the right note by tightening or loosening your lips.
If you're tooting a high note like a trumpet, you may either be holding your lips too tight, or blowing too hard. You're not trying to move the air through the tube, you're just trying to get it to vibrate.
Don't hum into the tube. (At least, not yet.) That's not how you get the drone started.
If you've found the right vibration, you should be getting a low, rumbly note out of the didgeridoo. It should be easy to maintain the note with just a little bit of air pressure. This is called the drone.

Tips
Once you're comfortable with the basic drone, you can change the shape of your mouth to coax some different sounds out of the instrument. Try mouthing vowels while droning, like, "Eeeeeeoooooeeeeooooo."
If you feel up to a challenge, try adding a little bit of vocalization while keeping your drone steady. Humming, barking, or singing down the tube while droning can get some neat effects.

Warnings
Remember to breathe! Take care not to get woozy or pass out. The way experienced players keep the drone going is by blowing out while breathing in, not forgetting to breathe in at all.
Check your didgeridoo for cracks. Some of the cheap mass-produced models are poor quality, and split easily. If there are any significant cracks, you probably won't get much of a good sound out of it. Sometimes they can be repaired with wax.

Things You'll Need
A Didgeridoo ( Of Course)
Someplace calm and comfortable where you won't bother anyone
A Glass Of Whatever You Want To Drink