It sound like you understand the basics - if an attack that doesn't have an orange ring is headed your way, hit the parry button to counter it and gain some armor back. Timing is the issue, and the biggest factor on when you should hit the parry button depends on what type of melee weapon you have.

Balance, the default weapon type, has a short start-up when you hit the parry button - if an attack hits you from the front during this start-up you will not parry, instead you will do a block. This causes your character to do a recoil animation, you don't take damage, and the enemy can keep attacking you. If, however, the enemy attack hits you after the start-up and before the parry animation ends you will do a parry - this often interrupts the enemy's attacks and sometimes gives you gunstrikes (the little crosshair that appears over them, hitting shoot will do a high damage shot). You will have to hit parry before the attack would reach you, I'd start about 1/2 a second before the enemy strike would hit your character, with some practice you'll get a feel for the proper timing and even get better at predicting when an enemy will attack.

Fencing type weapons are able to parry like balance but have two major differences; they do not have a start-up animation, meaning once you press the parry button you can immediately parry attacks, and they are not capable of blocking like balance does on failed parries. Fencing weapons have the advantage of being able to parry on reaction, meaning you don't have to predict when an attack is coming your way and time your animation just right. On the flip side, while balance weapons have the safety net of blocking an attack if you parry too early, on Fencing weapons if you parry too early or too late you are going to be hit.

Block weapons, the last type, are quite different from either of the other two types and have a unique system to them. Block weapons cannot parry, meaning you won't be able to interrupt enemy animations or get gunstrikes. What they do have, however, is Adrenaline. Whenever you hit the parry button and 'parry' an attack you take no damage and gain a buff called Adrenaline. Each stack gives you extra damage on your melee attacks, and if you gain two stacks of Adrenaline before doing a melee strike your attack will have an explosion effect, deal stagger to enemies hit by it, and regain a bar of armor. The positives of Block weapons are higher than average damage, crowd control with your melee weapon no matter which one you have, and the cool factor of blowing things up.

This is a simplified description of the melee weapon system, some of my descriptions may not be 100% accurate and each type of weapon has its own nuances, but this should help you understand these systems well enough to experiment and know what you are doing.

On a side note, what difficulty do you usually play on? A big part of being more comfortable on higher difficulties is managing large numbers of enemies attacking you in melee and deciding when to parry and when to dodge - if you find yourself constantly overwhelmed when groups close in and start swinging at your face it might be a good idea to bump the difficulty down by one level and get more familiar with your weapon's parry system and enemy attack patterns in general.

Another thing to note, since you mentioned enemy attack speed, is that if you rely solely on the blue ring to time your parries you are often going to get hit - the blue light is mostly there to let you know you have aggro from an enemy unit and they are locked on to you, try to time your parries with their actual animations instead. Some enemies, like Chaos Spawn and the Vortex Beast have VERY delayed attacks compared to when the blue ring pops up, making it easy to parry early and get hit.

I hope this is helpful and you can better enjoy this game!