We all play slightly out of tune so that we can modulate keys - equal temperament. We are just used to it.
The best way to tune a guitar (without a digital tuner) is to pick the string that has the most accurate intonation at the 12th fret and tune that string to pitch. For convenience, let's say it is the the A 5th.
You can then speed tune using harmonics starting from this string to get the other strings close to pitch, but any harmonics from the strings will be natural, not equal tempered, intervals. So if you use harmonics to tune starting from the bass strings, you are going to have trouble getting your B 2nd and E 1st in tune as tuning errors (in equal temperament) will compound as you go along bass to treble.
Once everything is more or less in tune go back to the most accurate string, in the example here the A 5th. Assuming that the frets are accurately placed (impossibly rare for them to be misplaced) and that you are not using tall jumbo frets with super slinky strings that cause notes to intone sharp, all notes on the A 5th will be perfect equal tempered intervals.
Then fine tune the other strings to the A 5th using octaves. Tune the E 6th string to the 7th fret on the A 5th and the D 4th to the 5th fret on the A 5th and so on. All open strings will then be in perfect equal tempered intervals in relation to the A 5th, our best intoned example string.
Depending upon the guitar, this state of tuning may be acceptable. It depends upon how good the 12th fret intonation is on the guitar's other strings and upon how much warmth from choral dissonance you want. You may want to put some strings slightly out to tune to improve intonation further up the neck, averaging out intonation errors. Also perfect equal tempered tuning can sound very cold. Run screaming from a piano tuner who uses a digital tuner rather than his/her ear.
I usually go around the neck playing octave intervals, major and minor 3rds, and 5ths looking for things that don't sound right to my ear and then doing micro tweaking.
I have a Snark head stock digital tuner and a table top Korg orchestral digital tuner with a variety of different temperament schemes. The Korg is more accurate than the Snark, but neither removes the necessity (for me) of selective micro re/de-tuning for warmth and playability all along the neck.
As strings get older, I find that digital tuners become less and less reliable. They become confused by changes in string vibration caused by wear. Sometimes they jump back and forth between the fundamental tone of the string and one of its harmonics. Your ear is better at picking out the fundamental tone. Old strings can sound very nice. Slightly out of tune is warm like a choir of human voices.