How does distance energy healing work?

Everything is energy.
Energy flows where attention goes. (Or "energy follows thought.")
Energy/attention can be directed to initiate natural healing. 

A common question that folks have when first learning about energy work (Reiki, dowsing, etc.) is..."how does it all work?" Distance energy work especially seems to be a matter of interest.

Let me be the first to say that the exact mechanisms are not understood. However, we do know (and have a wealth of evidence and research to support) that it does work!

There are a few concepts that may help you develop an understanding of what's really "going on" with energy healing and distance energy work. Gregg Braden and Pam Grout, among other authors, expertly discuss some of these in their work. Here are a few ideas to get you started.

Intention 
The power of "intention" is the power of our focused thoughts to affect reality. The power of intention has been demonstrated to cause healing in person and via distance. Medical examples and meditation experiments are particularly interesting.

Universal Consciousness ("Collective Unconscious" / "Unity Consciousness")
Whatever you call it, Universal Consciousness refers to a shared pool of knowledge and understanding that we are all connected to (or that we possibly create and maintain through thought). This force is one example of our innerconnectedness. Though we may "feel" and believe that we are separate beings, concepts such as the Universal Consciousness suggest otherwise.

Examples and Ideas for Further Reading
Quantum Healing Experiments
The Research behind Reiki
Experiments regarding the Vibration of Water
Quantum Entanglement

Again, these are just a few ideas to get you started on this fascinating topic.