Instructions
The Ground Floor
Lay a 23 by 23 cobblestone foundation.
Build a partial outer wall in one of the corners nine blocks long by two blocks high. Build a short outer wall along the adjacent side three blocks long by two blocks high. Add a long cobblestone platform against that corner eight blocks long (against your longer outer wall), two blocks wide, and one block high. Add a glass wall along the inside of the platform eight blocks long and two blocks high.
Install two water wells against the top blocks of the short corner wall so that water flows down along the short platform, between the glass wall and the outer wall, and stops before it flows over.
Extend the long side of the outer wall three more blocks and add a block of height. Build a platform facing the water platform, but make this one two blocks wide, three blocks high and three blocks deep. Build the new platform with one block's space between it and the water platform. Place two ladders on this platform on the top two blocks facing the water platform. Build a glass wall beside the new platform (three high and four long), facing the inside of the room, and wrap that wall around the platform to encase its inside in glass. Place two lava springs against the glass back to make this platform your lava platform, or grinder.
Create a water channel on the floor running toward the room's center. Use the space between your two platforms as the channel's source and set four glass blocks out from the glass encasement wall on either side of the channel because water travels eight blocks before stopping naturally.
Copy this grinder-and-delivery system design for each of the four corners to finish the first floor. Fill in the rest of the outer wall.
First Floor and Additional Floors
Build a two-block deep floor/ceiling extending nine blocks out in every direction from the top of the ground floor. Leave 2 by 2 holes above the corner water springs you've created so that mobs can fall through and be pulled along toward the lava grinder.
Dig channels eight blocks long and two blocks wide extending out from the 2 by 2 holes you've left in the floor. Place two water springs at the ends of each channel such that the water flows toward the holes but doesn't fall into them.
Build an outer wall at least two blocks high. Build as many more floors like this first floor as you like, but don't set the holes in the upper floors over the lower floor's holes so that the mobs don't fall too far and die.