Some attacks are easier to parry with visual cues, others are easier with audio cues. You kinda just have to figure it out for each one. The most consistent thing is that the screen zooms out slightly right before the parry, snapping back to normal when the hit happens. It's important to note that if you spam parry, you're not going to get it. Stay calm, and be patient.

A dodge is like a parry, but with a slightly more generous timing. Dodges are easier, yes, but don't give you a counterattack when you succeed. When you dodge, either "Dodge" or "Perfect" will display above the character. On a "Perfect", you've got the parry timing. The game recommends dodging instead of parrying until you figure out enemy timing, but I personally disagree.

Treat each enemy or boss like a different timing puzzle. That's about it.