My three parrots are all micro-chipped. It is quite simple. Take them to an avian veterinarian. My parrots had absolutely no reaction to the micro-chipping. Ana Grey my smallest grey was only about 290 grams when she was micro-chipped when she was about one year old. She is now 5. I can take my parrots back and have them scanned for their chips anytime I want. They are registered with "Home Again" so if they are lost they can be taken to any veterinarian with a micro-chip scanner or any humane society and I can be contacted. It is against the law to knowingly keep a micro-chipped pet and the offender can be prosecuted, at least where I live that is the law.
As for cost, of course, it will vary. My parrots, of course, where deemed healthy by the vet before chipping and it cost about $65, if I remember, for a total of around $100,including check-up, but that was 3-5 years ago in Washington State. I also asked that they not be sedated, as I believe that is more harmful that a poke by a needle.