The actual damage done is a product of the attack's base power, pokemon's attack stat, its level, modifiers (like super-effective) plus a little random variation.
Apparently this is the exact formula. I've broken it down into a few chunks to make it easier:
DAMAGE = ( USER_ATTACK ÷ OPP_DEFENSE + 2 ) × MODIFIERS
where:
USER_ATTACK = (2×USER_LEVEL + 10) × USER_ATTACK_STAT × BASE_POWER
OPP_DEFENSE = 250 × OPP_DEFENSE_STAT
MODIFIERS = SUPER_EFFECTIVE × STAB × RANDOM
variables:
USER_LEVEL is the user's current level
USER_ATTACK_STAT is the user's Attack (or Special Attack) stat
BASE_POWER is the power of the move, given in the movedex
OPP_DEFENSE_STAT is your opponent's Defense (or Special Defense) stat
SUPER_EFFECTIVE is 2 for single type advantage, etc like our type chart
STAB aka Same Type Attack Bonus is 1.5 if you used a move type same as your pokemon (e.g. Blastoise using Surf)
RANDOM is just a little random variation which makes it more interesting ;)
