This is essentially the same as tuning by what we’ll call the “normal” method (tuning the A string to the 5th fret of the E string, etc.). The difference is that you use the harmonic notes to tune between the strings. I’m assuming you know how to do harmonics. The easiest places to produce them on your guitar are at the 12th, 7th and 5th frets. The thing that you may not know is exactly which notes are produced by harmonics. Let’s take a look:
So you can see that if you sound the harmonic at the 5th fret of the low E string, it should be the same as the harmonic at the 7th fret of the A string. Likewise, to tune the D string you would match the harmonic at the 5th fret of the A string to the one at the 7th fret of the D string. The reason a lot of people tune this way is because the harmonics, when properly struck, will ring for a fairly long time, usually allowing you to tune it before it stops echoing. Also, you can use one hand to sound both harmonics simultaneously.
A few things to watch for:
First, you still have to get at least one string in tune to an outside source first. Otherwise you will be in tune to yourself but not necessarily the other people with whom you’re playing.
Second, the B string still requires special attention. People approach this in many ways but I think the easiest it to match the open B string (no harmonic) to the harmonic at the 7th fret of the low E (6th) string. They are the same note and it will be pretty easy to tell if they’re not. Other people prefer to match the open high E (1st string) to the harmonic at the low E (6th) string and then work backwards to get the B. Some people just do it the “normal” way.
Third, if your guitar’s intonation is very off, this won’t work. You will go through all this to get in tune and then cringe in disbelief when you strike any first position chord. It’s pretty rare for a guitar to be off by that much but it has been known to happen.
This is not any more difficult than the “normal” tuning method. A lot of people use this method because you can let the harmonics ring while you tune the string. You can use both methods – the “normal” way to get in the general neighborhood and then harmonics to fine tune.