How low? (action)

[Brooke]

I've always thought that higher action was a win-win once you got used to it. However, I've been reading up on intonation lately, and I now believe that lower action provides for better intonation. The reason is less compensation because of less stretching of the strings. Who knew.

you give some here, and take some there...

[nhspike]

Eyeball down your neck, and make sure it's not dead flat, or worse yet, curved the wrong way (towards the back of the guitar).
It should have a slight bow, or relief, so the string can vibrate naturally.
This can be adjusted by relaxing or tightening the truss rod.
Tightening fights the string tension, loosening let's the strings bow the neck.
1/8 turn, re-tune, re-check... slow and patient.
I find that when adding tension to the truss rod (flattening the neck) it's best to relax string tension... you can do this with by depressing the trem, or loosening string tension.
When relaxing tension on the truss rod, the strings will do the work for you (bow the neck more).
I still relax tension/whack the whammy bar out of habit even when looking for more relief.
It's best to let the guitar get used to it for a day or two sometimes.
I've had some guitars take a week of little tweaks to finally come around to my way of thinking and get stable.
Also, check the height of the nut... they are often to high (even shimmed too high).
Yes, one can be too high.

Strings should be very close up at the first fret.
If the nut is too high, you'll never bring the action down regardless of the neck relief, or bridge altitude...not without buzzing/fretting out anyhow.

The last obvious thing to check for is worn/grooved frets, or even a fret that is coming out of the fingerboard/higher than the others that needs attention.

Leveling is pretty easy to do, but one must work carefully, and frets may required additional work once leveled (re-crowning) if you want good intonation.

Work slowly, be patient.

Just my 2 cents!