While holding a one-hand-weapon. Walk over an other one-hand-weapon and hold Y to dual wield. The one you were using is now on your right arm and the new weapon is now on your left.
To fire your weapons, hold down the corresponding triggers but while you do this your aim is less accurate and you will get alot of recoil (when your firing, the reticle will move upwards making it harder to aim)
To stop dual wielding, Press B to throw down your left arm weapon or press Y. (I think if you switch to your holstered weapon, your left arm weapon will be automatically discarded...)
I think you press X to reload both weapons, or you can just let the clips run clean out of ammo.
So basically, while dual wielding you sacrifice your ability to melee attack and use grenades.