Seeing as Slimes don't spawn above Layer 16 in Beta 1.6.6 (our version), you'll want to start at Bedrock level to make your farm. The only advice I can give, is to start making one wide, by two high, tunnels (placing torches on the walls to keep monsters from following you around), listening for "squishy tramping" sounds (like walking on dirt, but sloppy-squishy sounding) and bumping around in the walls. You'll have to do your hunting in "Easy" or harder, difficulty, though... because Slimes don't naturally spawn on Peaceful mode.
Most people take a wild guess at a "Slime Chunk" and dig a 60x60x7 hollow at Bedrock level, and hope they get lucky. I got extremely lucky, and found three spots in my Slime Hollow that spawn Slimes.
It'll take some serious patience to find your Slimes. So good luck.
Nope, not in this version at least. I have had my slime chunk exposed and no slimes have spawned ever on peaceful. Seeing as that feature deals with monster spawns rather than terrain generation, you would not have to start a new world for it to be implemented. --- GT: Deadlock25
The only time I have ~ever~ seen Slimes on Peaceful, was when I saved my game (after I ~thought~ I wiped out all Slimes in my Hollow) and swapped difficulty to Peaceful to regain some health. I heard a Big Slime bouncing around on the other side of the wall, and after freeing him, I found that I couldn't actually hurt him. I'm not sure what ~that~ was about, but it was interesting having a Big Slime bouncing about all immune to damage.
I jumped back to "Easy" and split him down to Tiny Slimes, and harvested a bunch of Slimeballs off of that fool.
Do you have proof of this? I'm not trying to be a jerk or anything, but I spent ~several~ hours trying to make Slimes spawn in my Slime Hollow (after it was complete, with no changes made what-so-ever to it) in "Peaceful" mode. I followed all the steps I've done on Easy and Normal modes to make my Slimes appear (which worked on those modes), in Peaceful... and saw nothing other than that ~one~ Slime that wasn't supposed to be there in the first place, that I mentioned (and to be fair, I'd saved shortly after killing a Slime that ~was~ in the room, so it's only logical that the one I didn't see behind the wall would be there).
If Slimes ~can~ spawn on Peaceful, without having saved your game in Easy and having them show up by mistake, then I'd actually love to know how to do that, because it cuts down on the possibility of hostile mobs spawning, and interfering with Slime hunting.
You can try this one: http://extension.ws/minecraft/slimes.html
Or this one: http://mcslimes.appspot.com/index.jsp
I do ~not~ know how well they work... the ONLY map I have ever 100% confirmed the location of Slimes on, was the Tutorial seed, and until the update that gives you the seed ID details, I can't claim either site to be 100% accurate on Slime locations.
That said, I ~can~ confirm that the seed ID ~is~ accurate (to prove this, type in "worstseedever" as your seed, the seed ID will be "-1446162294", which when used on the Xbox 360 Edition, gives the same exact map with both seed IDs). So if you can figure them out, chances are, you can find your Slimes.