How do you make an automatic sugar cane farm?

You could try using a hopper clock, where one hopper passes to another hopper and then back again, with a comparator connected to one of the hoppers. Then, place a piston aimed toward the SECOND block up on the sugar cane, and connect the piston to the comparator. This means that when the sugar cane grows, the piston will immediately push it off and turn it into an item. Put a couple hoppers around the sugar cane to catch the item and move it into a chest.

I'm not sure if this is what you need, since you didn't give enough information about your gamemode, version, etc, and also I am not positive that this method would even work successfully without certain mods with your current setup, but it is DEFINITELY worth a try!

Here is a diagram of a standard sugarcane auto-farm:

Notice the flowing water in the middle. This should lead to a hopper connected to a chest for storage. You could even add an underground hopper circuit system and a storage room connected to it.

UPDATE: Changed pic to show a sugarcane farm instead of a wheat farm.

Here is a solution I like to use. I will show two different setups. One is minimalist. Easy in survival. The other is the same basic design but a little nicer.

Here is the minimalist farm:

Observer fires when cane on end grows to 3 tall. All pistons extend. Cane falls into flowing water which leads to hopper. Auto harvested cane ends up in the chest.

Here is another view:

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Here is another based on the same harvest system:

Here is a view of the lower portion:

This design has full source cubes behind the growing dirt as I read it grows faster if directly touching a source. Otherwise, it isn't much different from first design.

These designs are not fully efficient. When the pistons extend, sometimes the harvested cane lands on the dirt instead of in the water:

A fence over the water helps but doesn't completely fix the problem:

If you want a lot of cane and have resources, you can stack multiple farms on top of each other. I have made a tower of farms before.

For faster growth, make sure all growing dirt is touching a water source cube and provide extra light. (These do well underground as well)

Another option I have used it to use a railway with a hopper cart under the farms that collects and goes to an unloader. This option is the best if you want to make sure none gets stuck on the dirt and despawns. This also allows for very large farms with one collection point.

If anyone is interested in either of the big farms, comment and I will add another answer with the bigger farms.

Well, its pretty simple really. you need to have sugar cane growing (next to water of course) and you need to have pistons facing the sugar cane, but 1 block above it. on top of the pistons, place observers also facing the sugar cane. finally, place blocks on the back of the pistons with redstone dust on top. when the sugar cane grows to be 3 blocks tall, the observers will detect it and power the pistons, which will break it leaving 1 sugar cane at the bottom so that it can grow back. i recommend having a minecart system underneath and placing a wall around the sugar cane, that guarantees that no sugar cane will be not picked up.

heres a tutorial on how to do this if the instructions are difficult to follow just from my answer. if you have any other questions, feel free to ask!