Minecraft – Where do you find slime chunks

Any mob trap within 16 blocks of the bottom of the map will catch slimes as well, but you have to be careful to not hurt the slimes too much to get them to split the most. Punching and drowning are the safest ways to ensure that they'll split into more slimes. Also, you want a large room so that bigger slimes will spawn which can then have more splits.

The most important thing besides the depth is that it's in a chunk suitable for slimes. Slimes can only spawn in 10% of the chunks, picked randomly depending on the seed. You can calculate which chunks are suitable with this tool by trunkz though: http://www.minecraftforum.net/topic/397835-find-slime-spawning-chunks/

They only spawn a tenth as often as other mobs, but they'll also spawn in any light level, so if you're digging for diamonds at bedrock level, you'll usually find quite a few naturally.

Have you ever seen a slime in your farm? If answer is no, good chance you got something wrong somewhere in your calculations.

If you have seen a slime, then very likely there are just too many other places for MOBS to spawn in the 150x150 region around you, that fill up all the MOB slots. Time to break out the torches, and start lighting everything around you.

What I have found best, is to just let it sit for a long time while I do something else in the region, then revisit occasionally. This helps, because slimes spawn more slowly than other MOBS, but they do not despawn like other MOBS, so if you have a good slime spawning region, they will continuously accumulate.... It can get crazy.