Zone Offense

First off, people should be throwing more. There's no reason that people should just be practicing forehands and backhands too. I know way too many elite club players unwilling to throw a hammer or scoober in a game. It makes your game better, it helps you mark better (if you can envision other throws besides the one the guy with the disc is showing, you can react faster), and it's easy to practice. So there is no reason.

Secondly, 3 handler zone offense is (for me) dead. I'm sure people will be running it for many more years to come, but the dump swing offense that slowly moves up the field is only useful if you're not practicing those upside downs and blades. Even when conditions are great and the defense isn't putting much pressure on, it's still hard to complete 100% of throws. For most people, trying to complete one hundred 99% throws isn't a recipe for success. Statistically, it actually happens less than 40%* of the time for most players.

Now, there are 4 handler zone offenses and 2 handler offense, but my preference is for 2 handler. Among the zones I have played and preferred, there are 4 positions in a good zone offense: 2 handlers, 2 poppers, 2 wings, and 1 deep. For all positions, the check down list that people should go through every time they have the disc is to look for poppers, then deep, then wings, and then back to handlers. And most importantly, never look away from the disc, no matter who has the disc, where you are, or for any reason.

Handlers

You are the field general. That means you're responsible for A. throwing any throw that's less than 100%, B. pushing up the field so that you can always provide a reset, and C. seeing the field so you can adjust other players to be where you want them to go. People should be looking at you every time you have the disc and back to you any time you don't. Don't hold it for too long (I'm guilty of this), but don't lose opportunities because you were swinging it. Fakes are your friends, even if they're small fakes. 

Poppers

See my entry on poppers. In this particular Zone O, also make sure you're never behind the handler (or the play).

Wings

Stay on the sidelines. You can move up and down those sidelines, but stay on them. Give yourself a 3-5 yard cushion so that a hammer slightly over your head is still in bounds. Once you get the disc on the sideline, move it back towards the middle as fast as you can. Stay closer towards your attacking end zone when the disc is not on your side of the field, stay closer to the handlers when the disc is on your side of the field.

Deep

One of my favorite quotes about deeps in a zone is that if you're doing it right, it won't look like you're doing much of anything at all, but if you're doing it wrong, you'll clearly mess up your team. Stay far away from the disc to create more space for the poppers; come towards the disc once it past the initial wall or cup; make noise or somehow get other players to cover you so that there's more space in the middle of the field; finally, just keep moving around since you never know when a deep shot will come up.

Zone offense is easy.

* - 0.99^100 = ~0.37. Even 0.999^100 is around 0.9, which is not how frequently you want to be able to score when the other team is explicitly showing you where there are not defenders (considering you can apparently complete a pass 99.9% of the time)