For a complete explanation, please look at my answer to this post.
When you only have 1 weapon equipped (no offhand) then the damage will be completely determined by the dps of that weapon.
When you have 1 weapon and 1 shield equipped, the damage will be the same as if you didn't have the shield equiped (so the same as above).
When you have 2 weapons equipped, the damage will be completely determined by the dps of your right-hand weapon. However, since you have 2 weapons equipped it will give you more damage than if you have just 1 weapon equipped, say, as a sort of bonus. I believe the amount of 'bonus' to be equal to floor(dps of righthand weapon / 10), however I couldn't do many tests on that statement so it's best to take it with a pinch of salt.
So: always equip your highest dps weapon in your right hand and depending if you want more dps or more survivability you can choose a weapon (any weapon, stats don't matter *) or shield as offhand.
*except if that weapon gives you bonuses such as dual-wield modifiers, %damage, ...!
The DPS in arcane statistics is the most accurate estimate, because it takes into account your stats, buffs and skills, and that's what's used for skill damage.
But if you're playing on a higher difficulty and/or with enough players, don't ignore the individual hit and elemental damage, either, since enemies there tend to have enough armour to negate weaker hits. Sometimes, a lower DPS weapon with stronger individual hits is more effective than a higher-DPS one.
Best Answer
If you look in the bottom tab on the left side of the screen, you'll find the Arcane Statistics. The top of this tab includes detailed information about your offensive capabilities. The first set of stats include a critical damage bonus that applies to all the weapons that you are holding at the time. Underneath, you will find individual stats about your right-hand and left-hand weapons.
I checked out my Berserker character, which has one weapon with a +20% critical damage bonus in my right-hand. The damage done on a crit includes the extra 20% bonus with the right-hand weapon, but not the left.