I am embarassed at how old this question is that I didn't see before, but I don't regret writing all this. Hopefully someone may find it useful.
I came into this question thinking that a being made entirely out of immaterial stuff (not composed of fermionic matter like we are) would be impossible, but upon further reading I'm not so sure...! This is quite interesting, at least. The following is based on my amateur understanding of quantum mech, so I welcome corrections.
An EM wave is just one or more photons. It's hard to say whether they could change their wavelength and direction of their own will without getting more specific about what our Being is made of. An individual photon travels at lightspeed so it does not experience any passage of time, and therefore its properties cannot be changed except by interaction with something else.
But multiple photons can interact with one another -- indirectly. This is two-photon physics. In short, one photon in a pair possessing high enough energies (extremely short-wavelength gamma rays) can spontaneously fluctuate, or change, into a pair of temporary "virtual particles". The other photon can then be absorbed by (or, coupled to) one of the virtual particles, and re-emitted in a different direction before the virtual particles change back into a photon.
In this way, we might perhaps conceive of... let's call it "hard light", composed of gamma-ray photons, arranged in such a way that two-photon interactions constantly loop back around in predictable ways, forming stable "matter" that is actually gamma photons constantly fluctuating, bouncing and re-intercepting one another. This seems VERY questionable under the uncertainty principle, but maybe it's doable, somehow. Humans would certainly not want to go anywhere near this thing, and just as well, since it probably wouldn't survive long in human living conditions either.
So we have some kind of material to work with. Would our hard light be capable of forming a creature with a metabolism?
I think so. Maybe. Photons do not have any electrical charge, and I have no idea what interesting physical properties might arise from a unit of "hard light", so I cannot say that their "chemistry" would work like human cells (which essentially do work by exchanging electrons around in chemical reactions). But you could still build a mechanical computer.
Humans are chemical circuitry, and I see no reason why mechanical parts of arbitrary composition could not also form a living being. Clockwork computers on Earth are limited by the fact that they are made of metal: high energies and complex operations are required to turn refined metal into cams and circuits. It has been done before, but gears made of refined metals don't occur naturally on Earth the way amino acids spontaneously form from carbon chemicals. But maybe our hard light is different, and microscale gear-shaft machinery forms quite naturally from it.
Our being would probably require some extraordinary living conditions:
- A source of extremely hard gamma rays.
- Staying far away from large concentrations of fermionic matter, like the stuff that makes up humans. Hard light gamma rays could be quickly absorbed by atomic nuclei, disrupting the being's structure.
So where could they live? I have no idea. My best guess is somewhere in the vicinity of a pulsar, or an active galactic black hole, that has happened to avoid contact with lots of regular matter somehow, for some time. It's possible we could contact them if we built our own strong gamma emitters, perhaps a GR laser, and they might be discovered using gamma ray astronomy.
So that's the basic mechanism of it: Hard light by way of two-photon physics. As for the details, go wild.