I've seen a number of youtube videos explaining how to use parry to initiate ripostes, but I have yet to see anything explaining the basics. Is it just a matter of striking at the right time?
To parry, you need to equip a shield or weapon that has the attack attribute "parry".
Assuming you are using a controller - While equipped, press the L2 shoulder button (shield is in your left hand). Your character will strike the shield to the left (animation depends on shield/weapon equipped).
Now comes the tricky part - To successfully parry, you need time your parry so that it connects with the strike of your enemy (so that you "strike away" the attack). If you were successful, you'll hear a sound and your enemy will slump to the ground. If you attack him while on the ground, you'll do critical damage.
Note: Every shield/weapon has different animations and different keyframes on which it actually detects a successful parry. Some have a bigger window, some have a smaller one. You need to experiment and practice.
It's the same principle as parrying in PvP. There are attacks that can't be parried like The Last Giant's attacks any other obviously "unparryable" attacks. Just practise on the Undead Hollows in Forest of the Fallen Giants, they are easy enough to parry.