Wikipedia actually has a pretty good description of which zone normal every-day things fall out on:
Zone System - Wikipedia, the free encyclopedia
Scroll about half way down the page.
Zone V (the middle) is what you would get metering on a gray card.
Each zone is a stop. So, say you spot meter on your hand (Zone VI, assuming that's you in your avatar) and zero the meter out. You would have to over-expose by one stop to get that in Zone VI (by zeroing the meter out, you placed it into Zone V). Or, say you want to meter the shadows and you want there to be just barely a little detail there - Zone II. If you zero the meter out on that, you would then have to under-expose by three stops.
It would be faster to not zero the meter out though - depending on how many stops your meter shows. On my main camera, it shows +/- 3 stops. So, instead of zeroing it out on my hand, I would just set it to one stop over-exposure. Or say I'm taking pictures inside and I want the walls/paper to be white - I would meter that so it shows three stops, maybe four over-exposure. I shoot film and then scan it though - so I like to lean towards over-exposure. A dense negative is easier to scan...
It would probably be a good idea to do a test shot though to see what the exposure latitude is for whatever camera/film your using is though. Print out or buy a zone chart, take a picture of it after zeroing the meter out on a gray card, then see at what point you can't tell where one zone stops and the next starts. That's your latitude.