true dual exhaust is one exhaust system per bank of cylinders. On a V type engine, that would be a manifold or header on the head, a dedicated pipe going to the cat, then muffler, then tail pipe. (some of the components could be omitted obviously) The other bank of cylinders has the same thing on it... separate from the other pipe.
Stock systems on a v type engine will *generally* have the manifolds on each head, then into a 'Y' pipe, where the left and right pipe come into one. then go the length of the vehicle. Some will have a single catilitic converter, others will have one per side, and some will have 2 cats per side, then the pipe merges into one with one muffler.
The reason for wanting a free flowing exhaust is to help it get rid of the exhaust... to make room for the fresh charge of air/fuel to come in. The old over simplification of 'look at your engine as an air pump' comparison works here. You can't pump air in, if you haven't gotten the old air out. MPG can increase too... but that is normally more of a theoretical increase, or too marginal to see in real world applications. One can go too far with free flowing exhaust too. Off idle performance (low end torque and throttle response) will suffer and even hurt MPG.
Many late model trucks with custom exhaust will have the stock single system, and get the muffler cut off, a louder free flowing muffler installed, then another 'Y' pipe to split it into two pipes, and have 2 tail pipes out the back. This is not true dual exhaust.
The X pipe and H pipes are custom pieces on a true dual set up, it connects the two systems without combining the two into one. The reason for X and H pipes is to help balance out the exhaust pulses and have a very very very slight increase in how the exhaust system scavenges the exhaust from each cylinder. This is actually getting into the more complicated aspects and into the higher power motors.
True dual exhaust systems are hard to do on most cars and trucks due to the computers running them. It is also illegal (at the federal level) to mess with the catilitic converter. This includes relocating it, or even adding more than the car came with. So if your car only came with one cat, there is no legal way to run a true dual exhaust system. Many states don't have inspections and so will never know what you've done with the cats, but it is still a possibility to get a rather huge fine for messing with pollution control devices. This is also why most exhaust shops wont do modifications like this. Once they do the work, they are liable for what happened to the items tampered with on your car.... and you are liable too if you are aware of the illegal mode... so the EPA can now fine two people.
There is more to it than just a loud muffler and the number of pipes... it is more of a science. It is easy science, but if not done right you wont get the benefits that you could get in a properly engineered system.