How do I get my business listed in Google Maps – Google Places?

I just discovered via a phone chat with a prospective client that our office location never made the move on Google Maps when we moved our business a while back. So now I see that in one case my business isn’t listed on Google Maps. Why not? For our other business in the same office, the information listed on Google Maps is wrong. How do I fix it?

I was surprised to discover that it’s pretty easy to fix this!