How to intonate an electric guitar correctly
Most people intonate electric guitars wrong. This is how to do it right.
The first thing to know is that there is no such thing as a perfectly intonated guitar neck. It doesn't exist. Yes, there have been things invented such as Ernie Ball's compensated nut (standard on all Music Man guitars and basses including the lower cost SUB models), but that type of nut "expects" you to use standard tuning and the recommended string gauge for it to work like it should. There is also such a thing as compensated frets which looked like "melted" frets on a guitar neck, which is an extreme method of attempting to achieve perfect intonation. But again, try as some might, there really is no such thing as perfect intonation on a fretted instrument.
What matters more is intonation location.
Choosing where to intonate pretty much means everything
The standard advice is to intonate at the 12th fret. I do not do this because it always results in many fretted chords sounding slightly out-of-tune.
Being I play a lot of fretted chords, I intonate at the 7th fret. On a 25.5-inch scale neck, which is what my Jazzmaster has, my chords always sound better when I intonate there compared to the 12th.
What this means is that when I intonate a neck, I do not aim for a perfect E-A-D-G-B-E but rather a perfect B-E-A-D-F#-B.
Should you follow what I do?
Only if your guitar is always "out" even when your strings are in tune...
...but it doesn't mean you should intonate at the 7th fret like I do.
If you are always playing "cowboy chords" and rarely go past the 5th fret, try intonating to the 5th fret and see if your chords start sounding more in-tune.
Or, if you routinely fret notes higher up on the fretboard but your notes are off just slightly, maybe intonating to the 10th fret would work better instead of the 12th.
In other words, the best thing to do is to intonate wherever you play most on the neck. You're either only playing the first 5 frets, playing in the middle or up on the high frets. I fret notes and chord often around the middle of the neck, so that's where I intonate.
Something else you can try is that on 25.5-inch scale necks specifically, tune down your G string and only the G by 15 cents when using standard tuning. If you don't have a tuner that shows cents, get the Korg GA-40 or the Korg TM-50. Or if you want to get a supremely good tuner, there's the BOSS TU-3 (not cheap but crazy-accurate).
A 15-cent detuning of the G is very slight, but on a 25.5-inch scale neck it can work wonders for making chords sound a lot better. This is true regardless if the guitar is made by Fender or not.