Parrying is not a versatile defensive technique like the others, but against some opponents it could be the best thing to do. In fact, enemies rudimentary armed with axes, swords or spears will not be able to do much against a block; you could even make them stagger after the attack.
So, how do you make a parry, or block if you prefer? It's nothing complicated: as long as you have a shield or other weapon equipped in your left arm, you can parry by holding the L1 button. Even a two-handed weapon allows you to lock, with the same button. If you have nothing to parry with in your left hand, your character will still make a movement at the pressure of L1, a sort of quick punch that will allow you to immediately counterattack if done with the right timing. But remember that you can't do any of this with your bare hands.
Parrying costs stamina and doesn't completely undo incoming damage, especially if you're blocking with a sword or two-handed weapon. The best equipment for parrying is, of course, a shield, which will dramatically decrease (sometimes completely zero) the potential damage of the enemy attack. A lot of practice is required to parry effectively, but once you manage the timing and situations that require this maneuver well, the fights will be simpler (although there may be something simple in Demon's Souls) and yours higher odds of surviving.
Keep in mind that it is often a risky technique and it does not always succeed. If you fail, take away the frustration and focus on quickly regaining your character's health.