So the method in the video is tuning the guitar to itself, meaning not necessarily CORRECT. The amp tuner or the tuner app can be extremely accurate, so unless you've developed perfect pitch, stick to that. A Snark clip-on tuner can be had on Amazon for $10-15. This one is my favorite:
Snark on Amazon
When tuning it to itself in a pinch, start by trying to find a song with a definite E or A note or chord, especially if it's held for a while. Then try to match your guitar's E or A string pitch to that. From there, you can use the method PG shows to tune the rest.
There are two things to listen for. The first is if you're going back and forth on the two strings is one definitely higher or lower in pitch than the other? If so, adjust the string you know is NOT in tune to the one that is (for example, if you've tuned the low E string to E using a Metallica song or something), then you want to see if the A string is higher or lower, and adjust it to match.
(NOTE: If you need to lower the pitch of a string, lower it past perfect and then tune it up to where you want it - if you just lower it until it's right, it will pull lower the first time you bend the string)
The other thing you're listening for is dissonance. That's a kind of "wub wub" sound that gets slower the further away from each other the two notes are. When you can't hear any dissonance, the two strings are in tune with each other.
Hope this helps, but really, LEARN this method, but only use it when you don't have access to a tuner.