Now the bridge and nut are adjusted for height (almost) it's time to check the intonation... the overall tuning of the instrument. We do this my adjusting the length of the string which is adjusted on the bridge by moving the saddle closer or further away from the nut.

You need an accurate tuner for this, a strobe is best if you have one, I use the strobe setting on my TC Electronic Clip tuner.

The idea is that you want to harmonic at the 12th fret and the note at the 12 fret to be exactly the same.

Make sure you are not using old strings
Do not press too hard when you hold down the note, just a normal light touch.

As Charlie explains there are some variables that might make it not work so well:

Old strings
Vintage guitars with strong magnets in the pickups can pull the string (particularly vintage strat style pickups)
It is likely to be different if the guitar is laying flat, so I usually do it with it on my lap as I would play it.

The general look is likely to be the String 1 (Thin E) and String 4 (D) will be closest to the nut with the next strings gradually going back. Along the lines of this visual guide below:

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A very rough guide you could set Strings 1 and 4 and then roughly judge where strings 2, 3, 5 and 6 will be.

If the fretted note is sharper than the harmonic then the bridge needs to go back a little, a clockwise turn with the screwdriver should get it moving in the right direction.

Remember to tune up after making even a small adjustment!

If you're not seeing any difference after making an adjustment, it might be worth lowering the pickup to rule out that it might be pulling (unlikely on cheaper guitar though!).

Any questions? ask them below!