Critical Hits & Misses
A raw roll of 1 is always a failure, and a raw roll of 20 is always a success. Unless a raw d20 result of 20 is needed to-hit, a results of 20 indicates a critical hit. A critical hit allows the attacker to add her Strength or Dexterity modifier (whichever is more applicable) to the regularly determined damage after conversion using Scarlet Heroes rules.
If Scarlet Heroes rules are not being used, then a critical hit occurs when a roll of natural 20 on a dodecahedron die isn't needed just to hit. First, resolve any exploding weapon damage dice. Then, mazimize the damage of the lowest-rolling damage die. Then, add any Strength, Dexterity, or magical bonuses.
For instance, Halitha the Duelist attacks using her rapier and scores a critical hit. She rolls a d6 and gets a 4 result. That translates to 1 point of damage. However, because it was a critical hit, she is able to add the modifier that applies to her Dex 18, so the damage becomes [1 + 3] = 4. Monster critical hit combat damage is handled differently. For every four full hit dice the monster possesses, one additional point of damage is done. Thus, if the PCs were fighting an 8-HD wyvern that scored a critical hit on a claw attack, the DM would determine damage normally and then add 2 more points of damage.
Generally, a monster has the attack bonus of a Fighter whose level matches the monster's hit dice. Put another way, a monster's attack bonus, barring a different bonus given in the monster's description, is equal to its hit dice. Partial hit dice should be equated to the next whole number — for instance, a 3+1 HD monster would have a +4 attack bonus.