You need to set the open string to be in tune, then you check the 12th fret for being in tune. If not, adjust it, then tune the open string again then check the 12th fret. If not in tune yet adjust. Then tune the open string again then check the 12th fret. If not in tune - adjust again. Repeat until intonated.

But a high nut will help make the lower frets sound sharp (FW is wrong here), so you need to get the nut slot depth right before you intonate.

This should either be done with nut files (don't use just sandpaper or you'll end up with wide slots that make the strings buzz), or by sanding the bottom of the nut until the slots are low enough.

You'll need to remove the nut, so if it's not already loose, tap it gently from the ends until it comes lose. Don't tap it forwards or backwards as you're likely to snap off the end of the fretboard by the headstock. Clean the slot and the nut, then sand away a bit at a time. Always rub the bottom of the nut on sandpaper that's resting on a flat surface. Don't sand by hand alone, otherwise you'll give it a curve. Keep the edges of the nut at 90° to the surface. You can keep the strings on when doing the sanding, just loosen them each time you remove the nut then retighten when the nut is back in place . String tension will keep the nut in place for testing.

When done, glue the nut back in with some PVA or Titebond.

If you've got any feeler gauges, hold the strings down at the 1st fret with a capo or tape. The string height at the 2nd fret is what you're aiming for with no capo for the string height above the 1st fret (but no less). Sand a little and often once you get close.

You can always make strings go slightly out of tune if you press really hard, especially if the frets are tall, so just play normally.