Q:

How does Iron Man's Arc Reactor work?

In the film we can see him making a miniature simplified Arc Reactor with palladium and so on.
I know it is like a mini nuclear reactor, but what exactly are its inner workings or principles?

A:

The ARC reactor is definitely fusion. The industrial size one on the Stark campus is obviously modeled after a tokamak-type fusion reactor, and Vanko's schematics at the start of Iron Man 2 reinforce this.  The one used in the base of Stark Tower in Avengers similarly matches a tokamak reactor.
Him making a tiny one that fits in his chest is basically magic.  That Stark's had one running for decades on the campus is super-science (in real life we currently don't have fusion reactors that generate more energy than they take in).
Although of dubious canonicity, during San Diego Comic Con 2014, Marvel had a science-focused MCU presentation.  They state: 

Although never permitted to investigate it directly, Dyches suspects that the reactor uses a tokamak design paired with low-temperature fusion. 

A:

It runs on Applied Phlebotinum (TV Tropes link). But the use of palladium seems to imply some kind of cold fusion, or at least inspiration therefrom. Another candidate would be triggered isomer release, but both of these are maybe a half level up from snake oil, unfortunately, at least in regards to actually breaking even in energy production.

A:

The ARC reactors shown are low-radiation source fusion reactors. This implies strongly LENR (low energy nuclear reactor), as does the use of palladium. 
The lack of high powered magnetic fields rules out traditional tokomak reactors.
That said, the brilliant glow in operation is counter to LENR, so it's some form of mid-energy nuclear reactor. 
According to the Marvel Wikia, it's a repulsor based fusion system.
That said, it's comic book physics. It works because the story needs it to.
Note, however, that while repulsor fields are as yet fantasy, the use of repulsors to cause fusion should work; magnetic tokomaks work by magnetic compression of hydrogen plasma. (At present, sustained fusion is an energy losing phenomenon - it takes more energy to generate the containment/compression than can be extracted from the resulting reaction.)
http://marvel.wikia.com/Arc_Reactor

