In this tutorial, it will be explained how to build a mob grinder in version 1.5.2 of Minecraft. This version has been outfitted around a skeleton spawner, but it should be possible with zombies as well. This grinder uses fall damage as the main method of depleting the skeletons' health to half a heart at which you can kill each with a single punch. In order to do this, the required materials are around a stack or two of redstone, a sticky piston, a button, a few buckets, one or two redstone repeaters, and around a stack of signs.
Step 1: Building the Area Around the Spawner
First of all, you'll have to find a skeleton or zombie spawner. It should be at least above 30 blocks above bedrock in order for it to work. Dig down two layers of blocks below the spawner on all sides. Then dig in the direction you wish to build the spawner. Dig that way at least two blocks forward in a way that makes the room look more like a rectangle. Then dig down one block where you just digging at the far end and continue digging until the whole end of that side is down one block. Now it's time to add the water. Collect water using buckets and place them at the opposing end at which you want the hole to be. Place water across the entire wall so that it looks it is flowing towards the hole. It should stop flowing before reaching the small crevice on the opposing side. Place a sign in the middle of the crevice against the wall and fill the crevice with water so that it appears the water is heading towards the sign. After it looks like what appears in the image, start digging down where the sign is around 22 blocks deep. The mobs will fall down that hole with around half a heart left.
Step 2: The Sticky Piston at the Bottom of the Hole
Once the hole is finished, build an area around the hole so that it is easy to move around and build in. Surround the hole with blocks (preferably glass). Dig two blocks out at the level where the mobs fall on the opposing side of the area you wish the mobs to come up at; that block is shown where the hopper is placed. Place the hopper where it appears in the image. Then dig two blocks under where the mobs will fall and build an area. Dig towards the area you want the mobs to come up at by 2 more blocks forward. Place water in the area two blocks under where they will fall so that the water appears to be moving towards where you want it to be. Then, once that's done, place a sign on the bottom part of the wall where the water is leading. Dig upwards from there up to the level you want to kill the mobs (preferably close to where the mob spawner is). Place water above the sign and continue placing a sign and then water above that until you've reached where you want to hit the mobs.
Step 3: The Redstone at the Bottom of the Hole
Place a redstone torch on a block right next to the sticky piston so that it always stays on. Then place redstone behind that block with the redstone torch on it and dig upwards close to the area where you want to hit the mobs. Once you've gotten to that area, place another block where the redstone is leading and place a button on the other side of that block. Make sure to add redstone repeaters throughout the area where the redstone is leading in order for the redstone to reach the sticky piston.
Step 4: The Place Where You Hit Mobs
Dig an area around where the button and hole upwards are. At the top of the hole, make sure water is placed there so that the mobs are pushed forward. Feel free to place hoppers under the area where the water leads so that you can collect the items the mobs drop, but they are not necessary. Make sure to block off the area around the where the water is leading except a small area where you can punch them. A cobblestone slab can be used to make that small hole. Once that's completed, the mob spawner should be up and functional. In order for it to work, wait a while and press the button to lead the water to the area where you hit them. If the button does not work, you may not be close enough to the mob spawner so that the mobs can spawn and fall down the hole.