The value used for the Combat check is determined by adding the investigator's net Fight skill value, with any special Fight or Combat adjustments they may have from Skills, Allies, or other cards, adding the total bonuses from up to two hands' worth of active weapons or spells, and finally adding or subtracting the enemy's Combat rating. This gives the total number of dice used for the Combat check.
Any roll which fails to make the necessary number of successes is a failure.
The difficulty for Combat checks against a monster is the monster's toughness. That is, when the Combat check occurs during combat against a monster, an investigator must roll successes equal to or greater than the monster's toughness in order to pass the check and win the combat. If the check fails, the investigator must take stamina damage from the monster's attack (barring any special abilities which enforcing different rules).