Handedness
Each weapon has a particular handedness, which determines how well you can wield it based on your size and whether or not you are using a shield.
Contents
ASEVP
Penalties incurred when wielding a weapon with a shield are almost all based on your adjusted shield evasion penalty. This is found by:
ASEVP = Base_penalty - (Shields_skill/(5 + Size_factor)
The base penalty is 1 for bucklers, 3 for shields, and 5 for large shields. Size factor is zero for most races, -2 for large races (trolls, ogres, centaurs, and nagas), 2 for small races (kobolds and halflings), and 4 for little races (spriggans and felids, although the latter can't use shields at all).
Thus, ASEVP becomes zero at 5/15/25 skill for most races with bucklers/shields/large shields, but at 3/9/15 for large races (although some cannot wear bucklers), at 7/21/- for small races (neither can wear large shields), and at 9/-/- for Spriggans, who can only wear bucklers.
Note that in addition to its own penalties, the ASEVP is also part of your AEVP (adjusted EV penalty), a value which is used to calculate, among other things, accuracy and spellcasting penalties. However, this article concerns effects of shields other than those from their AEVP; for the effects of AEVP, see the above article.
One-Handed
One-handed (1H) weapons are the most convenient weapons to wield, regardless of size. Any species can use a one-handed weapon with a shield, and will only suffer the standard shield penalties to speed (which can be negated through the Shields skill). One-handed ranged weapons, like slings, don't suffer any shield penalty at all.
The specific penalty for one-handed weapons wielded with a shield at insufficient skill is an added delay of min(1dASEVP, 1dASEVP). This is not generally very noticeable, although a character wearing a large shield at zero skill will notice a difference.
Magical staves, broad axes, double swords, tridents, demon tridents and trishulas are considered two-handed for kobolds, halflings and spriggans.
Morningstars, Long swords, scimitars, demon blades, war axes, and spears are considered two-handed for spriggans.
Two-Handed
Two-handed (2H) melee weapons simply cannot be used along with a shield. They usually deal extremely heavy damage to make up for this restriction. You may use two-handed ranged weapons with a shield, but you will suffer a severe penalty to the attack delay.
Kobolds, halflings and spriggans can't wield two-handed weapons except quarterstaves, lajatangs, bows and crossbows.
History
Prior to 0.12, there were two additional types of handedness: 1.5-handed (which could be used with a shield but suffered larger-than-normal penalties) and double-handed (which had even worse penalties, plus cut the weapon's base damage in half).