Main Hand vs. Off-Hand
Unless a character is Ambidextrous, they possess a Main Hand and an Off-Hand.
To-Hit Penalties
An Off-Hand suffers a penalty depending on the relative size of the weapon. If the Off-Hand weapon has the same Size Category as the Character, it suffers a -4 penalty. For every size category above this, increase the penalty by 4. For every size category below this, decrease the penalty by 2 until 0. Consider Small characters to be Medium sized for this.
Thus, a Human wielding a Large weapon in their Offhand suffers a -8, -4 if they wield a Longsword (Medium), -2 if they wield a Short Sword (Small) or +0 if they wield a Dagger (Tiny).
Skill Penalties
Any Skill Check where the character is forced to use solely their Off-Hand when they would normally use on their Main-Hand suffers a -4 penalty. This does not apply, for instance, to a checks involved in disarming an opponent, but it would apply if a character was attempting to write legibly.
Multiple Hands
If a character possesses more than two hands, assume half of them are Main-Hands, rounding down, and the rest are considered are Off-Hands. If the character possesses only one hand from their race, unless stated otherwise, this is their Main-Hand. If the character possesses a prehensile tail, feet or other unique appendages not as suited for grabbing as a hand, these are not factored into determining how many Main-Hands vs. Off-Hands the character has - these are all Off-Hands.
If a species has nothing that constitutes a hand but may still have some form of a grip, such as a snake or a slime, this is considered an off-hand for purposes of using weapons but not for purposes of other skills or attacks.
Unarmed Attacks
Brawling, Wrestling and Natural Attacks are considered one Size Category smaller than the Character's effective size and thus suffer a -2 penalty if they are considered in any way 'off-handed' - this includes headbutts, kicks and bites. If a character has Proficiency in a Natural Attack, it no longer counts as being Off-Handed.