How to tell if an item can be used in the off hand:
Information about an item will tell you if it can be used in the off hand ("Off Hand" or "Held in Off-Hand").
For those with Dual Wield capability, weapons identified as main hand cannot be used in the off-hand slot. Only weapons identified as one-hand or off-hand can be used in the off-hand slot. Off-hand items cannot be used in the main hand slot. Weapons equipped in the off hand generally do 50% less damage than they would do when equipped in the main hand, and many players equip speedier weapons that hit quicker to mitigate this effect. For most classes able to dual wield there are talents to reduce that effect (see Dual Wield Specialization).
Shield items can only be used in the off-hand slot.
Casters have available to them a variety of non-weapon off-hand items marked "Held in Off-hand" that they can use in their off-hand slot. These typically have two or more of a variety of effects including stamina improvements, intellect improvements, mana regeneration, spell critical % and hit % chance increases, and spell damage/healing improvements.
Two-handed weapons use both main hand and off-hand slots, but the off-hand slot will appear empty. If you have a two-handed weapon equipped, you cannot use an off hand item, unless you are a warrior with the talent Titan's Grip.