Witch farms are built in witch huts and are an easy and plentiful source of redstone dust, gunpowder, glowstone dust and other useful drops. The simplest witch farm involves making two 7×9 platforms with 3 air spaces between them; the uppermost at one block below the roof of the witch hut, and fencing an iron golem into each platform. The area for spawning witches is the roof overhang area and balcony. The platform can be made from hoppers to facilitate item retrieval.
In theory, a Witch farm could be built in 1.8 either using an iron golem to separate creepers from mob farm spawns, followed by a Sun room to kill both skeletons and zombies; or a lava blade trap to kill all but witches, as they have the power to drink Fire Resistance potions.
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Witches have more health than most mobs, and so require a drop of 32 to be absolutely sure of killing them. Their potion resistance and use makes them difficult to farm as a player kill. Drowning and burning are negated by potions, and crushing negated quickly by self-heal.
Since Witch Huts spawn on the world surface it is very hard to get the witches to die from fall damage. You could have an underground base, but what if you don't want to? After building the farm make sure to have a one-block area where all the witches go to, then build up 32 blocks. Make this into a 'tube' like structure, then put a sign on the lowest block. also put a sign on the entrance to prevent leakage. Put water on the second block. On the third block put a sign and on the fourth put water. Repeat this pattern until you have filled the tube. then make it to where the top water block pours onto a sealed pathway. after 8 blocks open up a hole at the end to drop the witches. If you would rather this end sooner just place a sign above the hole after the length you want. Make sure that the drop is 32 blocks. Also make sure to seal off the drop "pipe" and create a loot collector with hoppers. It is recommended to create a room around this to prevent hostiles from attacking you whilst grinding and from creepers blowing up your farm.
The following videos are advanced witch farms for well-established worlds with plenty of resources