This is a guide to change the headlight low beam and DRL (bulb) on your 9th Gen Toyota Corolla. This applies to all 9th Gen models and years.
Time: A couple minutes
Parts: Headlight Bulb #9006. Toyota Part #90981-13047. Cost $20-25 per bulb.
Tools: Rubber Gloves
First check which light is out by turning on the headlights (you don't have to turn the key!). Then turn the headlights back off.
Note: If both your low beam headlights are out, check the headlight fuse first.
Note: You don't have to disconnect the battery, however when you remove the lightbulb from the plug I recommend that the headlights are off.
Once you've determined which side is burned out, pop and raise the hood. On my XRS it was the passengers' side. Now look at the rear of the headlight housing from the engine bay.
You should see something like this (passengers' side)

I tagged the headlight and plug but I'll point out some other things in the picture:
Top Left: That's the highbeam bulb and plug.
Bottom Left: XRS ABS Control Unit.
Bottom Right: Windshield washer fluid reservior cap.
To take the bulb out you will need to disconnect the bulb from the plug. You will need to pry the two clips back (on the plug) that are facing towards the engine bay and slip the plug off. I managed by hand...
Pic of the plug in my hand, note the two clips on the plug

Now you can remove the headlight bulb. The headlight bulb is removed by turning it 1/8th of a revolution counter-clockwise. After that you may need to wiggle it back and forth to get it to come out.
Pic of the old bulb on the 2ZZ-GE
Note: DON'T TOUCH THE GLASS PART OF THE NEW BULB. THEY ARE
HALOGEN. If you touch it with your bare hands oil/dirt will be transfered to the glass and when the bulb heats up it may explode or have a shorter lifespan.
With any new light bulb: Take your time and be gentle with it, don't drop it!
Putting the new headlight bulb in is just the steps reversed.
The new bulb might be hard to turn 1/8 clockwise... give it a little bit of force if that's the case. Make sure the plug clips snap to the new headlight.
Turn your headlights back on and make sure the new headlight bulb works!
Back to normal again!