How do you prevent water from running into concrete cracks?

Plastic sheeting with gravel to raise the end of the drive-plant a shrub in it somewhere to help absorb the extra water,

Oh wow! That is not good at all. I would fill those cracks and find a way to divert the water away from the foundation of your house. Can you post a photo?

Well one way is to fill the cracks with a liquid rubber like flex seal. But you still need to deal your driveway. Use a concrete sealer. Or you could fill the cracks with DAP concrete & mortar filler & sealant it's Waterproof. But again I would come back and use a concrete sealer over the entire driveway. I hope this helps.

Fill in concrete filler

Buy dense foam filler strips at your big box store along with what is called "floating" caulk. Clean out the cracks, stuff the foam filler strip into the cracks with a screwdriver and then top off with the floating caulk. Learned that trick years ago from an episode of "This Old House" and it works.

You need to divert the water away from the driveway before you can complete a lasting repair. It sounds like the drainage was changed at some point and is moving water across your driveway. This sometimes happens when people install plant beds, add berms, or change the grade in some other way. Look where the water is coming from and how you can change the course of the water before it gets to the driveway. Swales are often used for this, also French drains. There are many solutions. Read up on grading and drainage.

There is a compound just for driveway cracks. It comes in grey for concrete, black for asphalt. Do use the foam tucked in first, then the concrete caulk on top of it.

There is a caulk for driveways, big box diy, it’s grey, and more runny than a window caulk, it gets down to the of the crack.