First, take apart the whole thing. The WHOLE thing. Remember where each piece goes, maybe label the under not-showing sides with masking tape indicating their positions. (you could leave the frame around the mirrors if you cover the mirrored surface with newspaper---either way, it takes some work). Take pictures if you need to.
Second take it outside and sand the entire surface REALLY WELL with coarse steel wool. I didn't do as good a job as I should have (rushing---and it was 100+ degrees on the days I decided to do it. Smart, I know.)
Third, prime with spray primer made for anodized metal. Ask someone at the hardware or home improvement store. If you can go to a strictly paint store, all the better. The primer I got was just alright. It bubbled in spots, but it's handle-able. Make sure you use a large drop cloth and weigh down the edges to prevent the plastic from blowing onto your drying surfaces. (yeah, that also happened). I sprayed two sides at a time and let dry then rotated. Let dry a little longer than the can suggests...maybe a couple days.
Fourth, spray with chrome spray paint. Follow the instructions precisely concerning drying and re-coating times. Be careful when touching. If it hasn't cured before handling, you will leave fingerprints. Found that out the hard way, as well! :)
The best spray I've found (and trust me, I've gone through about 5 different kinds) is this one:
Fifth, and optional, is to seal it with a clear coat enamel. I didn't do that and have noticed some scratches. I have read, in doing research, that the clear coat might take away the chrome look and just make it look gray. So, test it out on a hidden part. I suggest the under side of the track that faces the floor. It the past I've used a really good clear coat on a variety of projects and really loved the results:
As I said, I did not do this step, but wish I did. You may be able to receive guidance from the paint store people. All you can do is try.
Sixth and final step is reassembly. Not the most fun ever. Those mirrored doors are STINKIN heavy. Get some gentlemen to help!
You could do any color besides chrome, following the same basic instructions. You wouldn't have to be as particular about touching and drying times, either. But I would especially use the glaze on any other color. It would look so cool and shiny.
If I missed something, or was unclear about anything, please ask! I'm not real great at instructions---so I hope this is understandable! It isn't a quick project, but take your time and do all the steps and it will turn out FANTASTIC! (better than mine, for sure, since I was impatient).
Good luck and be brave!!