Singing with blades
Dual wielding seems to be a cause of enormous confusion, so a few points
First, while yes, the Dual Wield ability itself only gives a small chance to trigger, this isn't quite the whole story. The Dual Wield ability is giving a chance for BOTH weapons to hit at the same time, dealing full damage, modified by your abilities, each with a chance to score a critical hit.
The rest of the time, your hands randomly attack, with a 50/50 chance of either hand swinging (they do not alternate, it's random - you can try it yourself, stand still with Onslaught on your rmb and hold it down, watching the swinging pattern - you can even see Dual Wield/Cross Cut/Tumult triggering).
Your attack speed is averaged between the two weapons you have equipped, so if you have a very fast sword in one hand and add a slow club in the other, your attack speed will drop (causing a resultant decrease in DPS).
Keep in mind that the visible average damage/DPS/attack speed display isn't entirely accurate when it comes to figuring Dual Wield damage, because of the element of chance involved.
Another important point to Dual Wielding - as you are giving up a shield, the return in offensive power is substantial. First, you can wield two weapons, and this gives you access to powerful offensive modifiers that affect BOTH weapons. Have a weapon in your offhand with +50% attack speed and +30% physical damage? Both weapons get those bonuses. Further, because you can modify both weapons with Charms and Relics that can only be applied to weapons, you are getting an even larger offensive bonus.
A Dervish of Fury
Your basic attack calculation for damage dealt is fairly simple. Take your weapon damage, find the average, add any modifiers to physical damage, pile up all the mods and add them together, then take the Piercing %, convert from Physical to Pierce damage, pile up all the Piercing mods, then take any Elemental or other damage type damage, and (yes, again), pile up on all the mods on it. Once this is done, your target is smashed with X Physical, Y Piercing, Z Elemental/Bleed/Poison/etc damage. They get their armor and resists to decrease the damage, and finally their health is reduced (and possibly, keeps reducing, if you had dot damage in there).
All of that is pretty straightforward, and raising those modifiers directly increases your
average damage dealt. This is important, because rather than worrying about if you're dealing 500 damage per hit, or 550 damage per hit, what is often more important is the answer to a simple question: "How many hits does it take for me to kill a monster?"
And that's where attack speed comes in. Unless you can get your average damage to the point where all monsters are dying in a single hit, how
fast you deal damage can sometimes be more important than how much damage you deal.
Think of attack speed as a global modifier to all of your damage dealt. At 200% attack speed, you are inflicting twice as much damage in the same period of time, and this is where the Damage Per Second display comes from.
All weapons have a certain basic attack speed (some variance from the baseline 100% value). This value is modified by any Attack Speed or Total Speed modifiers affecting your character.
Theis would be pretty straightforward, with attack speed having an important, but not overpowering influence on your damage, if it wasn't for two facts: First, your attack speed affects the actual animation time of your attacks, which influences how quickly you can deal damage and then disengage from melee (extremely important for ranged characters for one thing, since melee is usually a bad place for them to be). Second, and of greater importance;
skills that have a % chance to trigger are NOT scaled to your attack speed.
That is, if you have a 10% chance to deal 50% more damage per hit, that chance is not on a sliding scale 'balanced' to your attack speed. It is ALWAYS 10%. And this means that attack speed can have a much greater impact on your overall damage output than it may first appear. Prize items that increase your attack speed if your character has many % based abilities that trigger when you attack!
Speed Caps
Player minimum speed is capped at 60%. Attack speed is capped at 50% minimum, 222% maximum (199% for dual wield), run speed is capped at 166%. Player minimum run speed is capped at 50% in Normal, 40% in Epic, 30% in Legendary (what, you thought it would get easier?).
Monster minimum speed is capped at 20% in Normal, then 30% in Epic and 40% in Legendary. Boss monster minimum speed is capped at 50%
There are a few types of speed in the game. There are three separate speed attributes: Attack, Cast, and Run. Many items only modify one of the three. Items that modify them all tend to use the term 'Total Speed', as do a few skills that give full speed bonuses. I believe there are a few cases where this is inconsistent however, and the skill may say 'Speed' instead of 'Total Speed' explicitly, but I believe those are still modifying all three speed types.
Resistances
Player resists are capped at 80%, and penalized by 40% in Epic, 100% in Legendary
Modifiers
The general rules of thumb for 'does this skill affect that other skill or weapon' are fairly simple.
If a skill is passive, it affects everything you do
If a skill is an activated buff or a constant aura, it affects everything you do (and potentially everything your teammates or pets do)
If a skill is a modifier for a base skill, it ONLY affects that skill.
A note for modders
I figured those of you working on Custom Quests might find this to be of interest: Check this record records\game\combatequations.dbr (just insert that directly into Import Record, no need to search for it manually), and you can then change all of the above formulas! There are also many other base game mechanic formulas that can be changed, including critical hit thresholds, hit location percentages, experience formulas, and others. Check records\game\gameengine.dbr and records\game\gamerules.dbr - and there are more besides
Enabling PVP!
This cat is out of the bag from the lead designer, so in it goes

Add /pvp to your launch shortcut to enable PvP in multiplayer
eg, "C:\Program Files\THQ\Titan Quest\Titan Quest.exe" /pvp
Only PvP enabled servers will show up in the multiplayer list, and you need to have it enabled yourself to join. You can fight anyone not in your group.