What factors affect soil hydration and crop growth time? What is the most efficient layout of dirt and water to grow crops?
Like Brant said, tilled soil will stay tilled if it has a water tile four blocks or less away. Even though a large field of crops would result in the quickest growth time, this is not necessarily the most efficient method of farming as you would need to crouch to avoid the trampling of crops, and it's not easy to access each tile.
There is a thread on the Minecraft Forums with various farm designs - here are two of them (credit to Hans Lemurson of the forums):
The tilled blocks are raised so you won't trample crops as you collect them, and the water tile in the middle ensures that all the crops are exposed to the water. The nice thing about this design is that you can elongate the design simply by repeating the middle row (the one with water in it). The walls of the farm serve a double purpose - keeping animals out and serving as a back wall so that harvest crops bounce back to you.
(Oh, and the chest at the door is good for storing excess seeds or wheat.)
This is a spiralled variation of the farm. The crops are one continuous "shelf", so can hold the mouse button and move as you are planting or harvesting.
To be hydrated, tilled soil needs have water up to four blocks away, either on the same level as the soil or one level above it. This means a 9x9 field with a single block of water in the middle will be fully hydrated.
Growth time is a little bit more complicated. The Minecraft wiki has more information including the formula the game uses to determine growth rate, but it would seem that the quickest-growing crops are those surrounded by crops on either two sides, or all 8 sides. In other words, plant in either straight lines or large fields.
I feel like answering this too even though its old (if i read the time thing properly but its confusing as there's no 4 numbered thing) as I've recently watched a video about this (link at the end, don't worry you wont have to get to any portals... that's a crappy joke but it works lol)
I'm explaining in my explanation for this post but watching the video after will help you too, so basicly if you want the most efficient farm, put the crops into rows like this:
w=wheat c=carrot S=saturator (something that saturates the farmland underneath the crops) -=this is just fitting the letters properly
If its either diagonal crops of the same type or its in both x and z direction it'll have 1.5 update ticks per second which is half the default block update speed
If its in alternating crop rows it'll have 6 update ticks per second which is 2x the default updates than 1 by itself
By the way if your confused on what I mean by update ticks per second use this command: /gamerule randomTickSpeed and it'll say its 3, the defaulted speed for update ticks and if you type a number after it will change to that, but I suggest not going over 1000 as the higher the number the more it needs to process
video link:that's not me I haven't started youtubing yet