Yeah, really: "without listening to it"...
Starting form basics in Standard (EADGBE) tuning, if you play the 5th fret of a string it should be the exact same pitch as the string below it. The only exception to this is the B string which is tuned to the G string's 4th fret.
Now that's a pretty common way of tuning a guitar - you make sure your E string's in tune and then tune the others to that.
But I can't hear pitches well thus that method doesn't work for me unless the string is massively out. So...
Tune your guitar as accurately as you can with a tuner and play the 5th fret on the D string and an open G string at the same time. You should hear it sounds quite nice. Obviously.
Now play the 4th fret of the D string and the open G string at the same time. Apart from sounding horrible you should be able to hear a slight pulsating sound in the notes. It may be more obvious if you detune 1 of the two strings half a semitone out and try again from the 5th fret.
You'll hear that as the pitches get further from the same the pulsating gets faster and as they get closer to the same pitch that pulses get slower.
Experiment by detuning 1 string and then trying to get the pulsating sound as slow as you can by retuning it. If it starts getting faster again, you've overshot and need to turn the tuning peg the other way. When you're done, check with a tuner!
Now then, I said we'd do it without listening to it.
Once you've got the hang of it put some headphones on and play some music or white noise loud enough that you can't hear yourself playing. Hold the guitar relatively tightly in your left hand (or whichever you hold the neck with) and play the 4th fret on the D string and the open G string as you did before. You should notice the pulsating again despite the fact you can't hear the guitar - this time though you're feeling it through your hand rather than listening to it!
I personally find feeling it easier than listening to it but you may find it's easier the other way. If you can't hear the pulsating then try amplifying the guitar and as I said try slightly detuning the string over and over (not too far though) until you can spot the difference.
Thanks for reading and I hope it comes in handy when your audience is too loud!