Teach players core values of spacing, screening, cutting, and passing. Zone defenses have weaknesses and screening informs parts of good zone offense.
The most common zone defense we see is 2-3. Coaches choose where and whom they wish to attack in the zone...and whom they want to get the lion's share of the scoring chances. Basketball is not a democracy.
Use screens to set up 'quick hitters' or create defensive indecision. We can categorize "zone screening" design to screen ball side, help side, or middle.
This FastModel play screens both the top and the bottom of the zone and occupies the other defender with the dribble. In addition to setting the quick 3, the play offers 4 off the roll.
Ball side and help side screens set up the skip pass, with closeouts limited by screens.
Screening both top defenders can free the point guard for midrange shots or to attack the 5.
Michigan State's Tom Izzo uses a pair of diagonal screens in "X" to create a lane for attacking the middle of the zone. 2 may have a shot, a pass across, or 5 on the roll for a bounce pass.
Another MSU play (Fist Down) screens the middle of the 2-3 with the goal to get the ball inside to the 3 who can score, or drop to the 5 or the 2.
Florida Gulf creates an overload situation and then (from a stack) screens both the middle and the top of the 2-3 to establish a driving situation or drive and kick for the three.
I like "Horns." Here's a horns sets versus the 2-3.
Regardless of what we teach, nothing works unless players can make shots, space the floor properly, and move the ball crisply.