Here is a basic sequence showing how to re-establish positioning after moving the disc downfield in a Horizontal Offense. The basic premise with re-positioning is to typically have a Handler fill in the position left vacant by the Lane Cutter. The main goal is to maintain the overall positions where the player with the disc always has 2 options to reset the disc to another Handler, as well as 4 options downfield for continuation passes (2 primary and 2 secondary).
This play below describes how to play zone O against a standard 1-3-3 zone. The basic principles of zone O are dump and swing, crash the cup, dump swing etc... The focus is to pass a lot and expose any openings in the zone that can lead to quick throws up field. It's actually very easy to break most zones if the offensive players are aggressive and are comfortable with cutting into tight spaces. A key component of a good zone O is that the two wings (4,5) work together to create space. One player (5) can act as a decoy cut to draw in players while the other player (4) crashes to get a nice short pass.
This play is for teams that have highly skilled handlers who can pretty much throw against any force in any condition. The play is pretty basic at the core and starts out as a basic stack down the middle. From here the back lane cutters make 45 degree cuts to the front. Any good defensive team should be able to cover these. The play turns into an isolation play after one more player cuts deep and leaves one player isolated in the middle. Here it should not be too difficult for the cutter to get open for an easy score, a good handler can just throw to space with a bit of float, or maybe a hammer/scoober. It should be noted that any of the first cuts are good looks.
This play is very unique and will not always work out. To preform well, you must practice this play a lot. The play basically involves your team to set up into a very tight circle once the disc is pulled to you. After this you simply, make very short passes inside of the circle while shuffling across the field making sure no one travels. The opposition is not allowed to crash the circle because that would be a fowl and it is possible that you could also call double team.
A useful play to use at the begininning of a game. If it does not work out, the disc is still set up at the other end of the field and it opens up the middle of the field later on because the opposing team may believe you will always huck.