In X-COM: Apocalypse, agents are able to wield two weapons simultaneously. The effects will vary depending on the game mode. There is no benefit to dual-wielding weapons in the original X-COM games created before Apocalypse.
Real Time Dual Wield
In real-time combat, if an agent is wielding two weapons at the same time, the agent's overall firepower will be improved. The agent's right hand weapon will fire at its normal rate while the off-hand weapon will fire at a slightly reduced rate. This will vary depending on the firing mode and the speed of the weapon.
Turn Based Dual Wield
If an agent has a weapon held in each hand, only the currently selected weapon will fire with the standard click and target method traditionally used in the X-COM games.
To make use of both weapons, you need to order the agent to shift-left click the ground or target that you want the agent to shoot at. Continuously firing the weapon this way will cause the agent to alternate the right and left weapons.
Unfortunately this way of firing the weapons offers no real benefit over firing a single weapon as there is no reduction in firing speed in addition to the accuracy penalty.
Dual wielding in turn based is therefore not as beneficial as in real-time combat.
Two handed accuracy penalty
Two handed weapons held in this way will suffer an accuracy penalty. One handed weapons like the Megapol Lawpistol, Megapol Plasma Gun and Toxigun do not incur the penalty because they are one handed weapons. Launchers are also exempt from the penalty even though they are two handed weapons because missiles are homing weapons and do not use the agent's accuracy stat.
Assuming Apocalypse roughly follows its predecessors in its accuracy calculation, two handed weapons will suffer a -20% overall accuracy penalty.
Firing Mode and Weapon Speed when dual wielding
If pairs of identical weapons are used, take into account the weapon's rate of fire when deciding on the firing mode. Toxiguns and M4000 machine guns have very high firing rates. If set to full-auto, the off-hand weapon may not get utilized very often. This wastes the purpose of dual wielding the weapon. To work around this, simply go to a higher firing accuracy mode such as snap or even aimed. The off-hand weapon will get fired much more frequently, so you will be able to combine the benefits of increased rate of fire and increased accuracy, which could be a considerable improvement over firing just one gun on full-auto.