How is energy really dissipated in an electric circuit? I've heard that in a circuit, energy is provided to separate components (lamps, motors, etc.) because of the flow of electrons. How is this possible? Since energy cannot be created, where is this energy coming from (i.e. what is it being converted from)?
Furthermore, is there anyway to describe this process using the Quantum Field Theory or by using Quantum Electrodynamics?
 A: The electrical power does not only come from a flow of electrons, but also because something pulls them : an electric field. We model this by defining the electric power received by a component as being the product of the current flowing through it by the voltage applied to it (in the opposite direction, by convention). 
As for whence the energy came from in the first place : it comes from something pulling electrons. Be it a moving magnetic field from an alternator, the friction between two materials (for static electricity), or a chemical reaction in which electrons play a part (like in batteries).
When it comes to theoretical derivation, I am only aware of classical models (like Drude's model for resistance). I'm sure there a way to predict such things with quantum physics but I have no idea how.
A: In all aspects of nature, movement (and more general stuff too) arises due to what physicists call potential differences. That's why one calls them potential: Because they have de potential of creating kinetic energy. In the case of gravitational potential energy, for instance, it can be converted to kinetic energy by getting rid of normal reaction forces (i.e. by letting an object fall). 
The electric potential follows the same rule, but instead of dealing with mass, it deals with electric charge. The electric field, just as the gravitational one, stores energy, which can be converted to kinetic energy when we expose a charged particle to it. Since electric charges can be positive or negative, the electric potential allows for both attractive and repulsive interactions between particles, while gravity is strictly attractive.
Your line of reasoning is quite correct: there cannot be electron movement without an exchange in energy. Energy must be added to the system in order for the electrons to move, and that's why we need to plug stuff in the power outlet: The outlet is what creates the potential difference in this case. A more sophisticated, outlet-less use of the energy present in the electric and magnetic fields employs antennas, coils or other wired structures to directly capture the energy of propagating fields. These fields are almost always invisible, but one of its manifestations is well-known to us all: visible light. What is happening inside your eyes right now, for instance, is similar to what happens in a wireless circuit: We have specialized cells that are able to generate kinetic energy from the electromagnetic field around us, as long as it falls within what we call visible spectrum. These cells generate electric signals from light and our brains interpreted it in a way we call vision.
All processes described above deal with light-matter interactions, and can be studied within the realm of quantum electrodynamics. It is in this context that the word photon emerges: Photons are related to the amplitudes of these electromagnetic fields, and in many interactions can be well described as being little balls - even though the fields propagate as waves. 
A: It comes from the battery. Or generator. Or you buy it from someone else who has a big generator.
Your circuit does have a battery in it, right? 
