Driving against a zone?
I don't think there is any play or way to break down the zone properly with a drive... Compared to man to man D where you can iso and the defense is guarding a man instead of a space..
majority of the plays that my team runs against zone is "high-low"

4 and 5 at the high and low post, ball is with the point

ball is passed to one side, 5 slides down and out abit to bring the defender and open up space for the 4 on the high post

The ball is skipped to the weak side...
If you were the 3 here you could
drive as you can see the defense has to shift and recover, but the 3 should prob take the open J

Now 4 and 5 do the same thing but on the other side now
1. The 4 now cuts to the low post and brings defenders with him
2. Then once the 4 is down there, the 5 cuts hard to the high post like pictured and is usually open..
3. can skip or pass to the bigs
The offense is good for getting shots...It is really just the 4 and 5 alternating and forcing the zone to shift, The perimeter players must wait for the 4 and 5 to get to the high and low posts before skipping, or else you don't shift the zone properly..
Theirs more detail, just look it up, but thats just the basics..
Their is other types of zones, which require different offense, but i doubt they would be using them in a local comp..
Then again, you could break down these Defenses yourself, if you aren't playing against the best competition..
The best ways to get into the lane are:
Develop an outside shot - Be a treat an the d will have to play you tight making ti easier to drive
Get a mid range game - say you get into the lane and their is a big guy waiting for you at the rim, and he stays home on the play.. just pull up.... You have to have a mid range pull up jumper.. this wi'l also put off the shot blocker with his timing and he won't know if you jumping or not
jab steps/Crossover moves/pump fakes - Develop more ways to beat your defenders, get some tools like a nice crossover and jab... make sure you never waste your dribble, you be surprised how much easier it is to penetrate with the triple threat position than a crossover..
If you have a good outside shot, the fake will really work
Finishing at the rim - Create contact, If the big guy is coming don't shy away from the contact and put up the shot early, thats how u get blocked.. Take it too his body and lean into him, so if he jumps you have the foul and you have protected the ball...
I played with a guy that was the master of the and1, he would always make sure he has contact before the ball leaves his hands.. and he always protected the ball first