There are four steps to setting the intonation once you have the bridge in roughly the right place.
To do that, measure from the face of the nut to the centre of the 12th fret and double it. Your saddles need to be that distance from the nut plus a small amount (on a Strat, maybe as little as 1mm) to allow for compensation (as you press down on the string you stretch it and so change its pitch).
Each string requires a different amount of compensation, and so you should aim at having at least a 3mm window to move them back from that measurement. From memory a Strat bridge gives you 6mm or so of movement - if so, set the saddles fully forward, and then that point should be nut-12th x 2 distance from the nut.
Intonation setting is as follows:
1. Set the relief in the neck - this is the curve under string tension, and is the only thing the truss rod should be used for. Fully strung and in tune, then capo the strings at fret 1. With the guitar held in playing position, hold down the low E string at the fret nearest the body join and then measure the height between the top of a fret near the middle of that distance (7th?) and the bottom of the low E. For a Strat you are looking at .004 to .008 in inches (.004 is the thickness of a sheet of printing paper). If relief is too great, tighten the truss rod 1/4 turn and re-measure. Too little, loosen 1/4 turn. Tweak from there to suit your playing style (strummers need more relief, shredders need a pretty flat fretboard).
2. Once relief is set, adjust the depth of the nut slots. Hold each string down between frets 2 and 3 and check the space between that string and the top of fret 1. If you gently tap the string at fret 1 you can tell how big the gap is. Ideally you want no gap at all (but plus an invisible fraction, because lower is very bad!), but a hair above the fret is safer - you can take it down further later if it feels like it needs it. Nut slots must slope down towards the tuners so that the string's last point of contact is at the face of the nut. Ideally, the bottom of the slot is rounded to match the string's shape. If you screw this up you'll have to make a new nut! If you don't do it, the guitar will play out of tune on the lower frets.
3. Set your preferred action height, measured conventionally between the bottom of each string and the top of the 12th fret. Each player likes a different action. For an acoustic, 2.5mm at the low E reducing to 2 mm at the high E will suit an average player (a heavy strummer might want more, a delicate fingerstyle player less). For an electric I'd work with 2mm-1.5mm as a starting point, but try playing it and adjust for feel, Too low for your style and it will buzz like a wasp. If the frets are uneven it might buzz anyway (in that case, fix the frets).
4. Finally, set the saddle position for each string so that the note at the 12th is exactly an octave above the open string. An electronic tuner helps here, but the 12th fret harmonic (plus a good ear when you play the 12th note) gets you pretty close. At a guess, this might be nominal scale (nut-12th x 2) + 1mm for the high E and nominal scale + 2.5 mm for the low E. Tweak from there until it sounds sweet. Heavier string require more compensation than light.
This order of operations is important - if you start with the saddles and then change the action at the 12th, the saddles will be out, and so on.
Important note: this setup only works for the gauge of strings you use. If you swap to a different gauge you will probably need to reset relief and tweak the saddles (but the nut should still be OK).
Second note: old strings can intonate badly because they are dented and/or stretched in spots. You might use old strings to get it close, and then do final adjustment with new strings fitted.
