What is the charge meter in Pokemon GO based on? Is it determined by damage, EPS, different attacks, or what?

Every fast attack gives a specific amount of energy each time you use it. This amount depends only on the attack you're using and not on how much damage you do or any other factors.

As far as I know, this information isn't available in-game anywhere, but fan sites such as Gamepress have them all catalogued - they list the values in the form of energy per second rather than energy per attack, though that's probably a more convenient way of looking at it. For instance, Lick gives 12 energy per second, while Fire Spin actually only gives 9.09 energy per second.

However, you can also see that Lick has a cooldown of only 0.5 seconds, and working backwards from there that means it gets 6 energy per attack, while Fire Spin has a cooldown of 1.1 seconds for 10 energy per attack. So even though Lick has higher energy gain per second, it has lower energy gain per attack which is why it seems like it gives less. But it makes up for it by being faster and giving more energy overall.

I did see something once that said you got 0.5 charge for every 1 HP of damage dealt. Is that correct?

You may have misread that, or the person who wrote it may have mixed things up. When you take damage from a gym defender or raid boss, you gain energy based on the damage that was dealt to you. But that is completely separate from the damage your own fast moves deal.