How to Find Slimes in Minecraft
To find slimes in Minecraft, first find a flat area in a swamp. Next, turn on your coordinates by pressing f3 and make sure the spawn area's Y coordinate is set between 50 and 70. Find a dark spot with a light level of 7 or less, then make sure there are at least 3 blocks of vertical space in the spawning area to let the slimes breed. Finally, retreat 24 blocks away from the area, build a shack with a bed, and wait for a full moon, which is when slimes will spawn.
Travel to a swamp biome. Swamp biomes are characterized by dark trees and grass, vines hanging from trees, and numerous bodies of water. You'll usually find them in ravines or as an extension of a forest biome. Find the flattest place possible. Swamps are generally flatter than most other biomes, but you'll typically want to find a flat, wide area within the swamp. Enable your coordinates. On Mac and PC, you can do this by pressing the F3 key; after doing so, you'll see a bunch of white lines of text pop up in the top-left side of the screen. On the console and PE versions of Minecraft, you'll need to open a map to view the "Y" coordinate. Make sure the spawn area's Y coordinate is between 50 and 70. When in a swamp area, slimes will appear between the 50th layer and the 70th layer. For reference, sea level is at the 65th layer. Find a dark spot. The light level of your chosen area must be seven or less. You can create an artificially dark area by covering a section of the swamp's canopy with a dirt block ceiling and walls, or you can just find an area with a low enough light level. You can view the light level by looking for the "rl" value in the second-to-last line of text when you have the coordinates view enabled. Make sure the spawn area has at least three blocks of vertical space. Slimes require two and a half blocks of vertical space to spawn, so you may need to clear out some foliage, which may in turn raise the light level. Retreat at least 24 blocks away from the spawn area. Slimes won't spawn if a player is within 24 blocks of the spawn area, and they will de-spawn if a player is 32 or more blocks away. Wait for a full moon. Slimes spawn most frequently during a full moon, so you may want to build a small shack with a bed nearby and wait for the full moon part of the cycle. Slimes will never spawn during a new moon. Try to force the slimes to spawn. By creating several platforms with at least three blocks of vertical space between them, you can increase the number of surfaces on which slimes can spawn. If you do this, make sure that all of the platforms fall within the 50- to 70-layer range! Search for caves below the 40th layer. If you aren't able to prompt slimes to spawn in a swamp biome, you may have more luck underground. Slimes spawn in caves located in "slime chunks", which are 16 x 16 x 16 block areas. You have a one in ten chance of coming across a slime chunk. Add torches to the cave. When below layer 40, slimes can spawn in any light situation; adding torches will both make mining easier and prevent other hostile mobs from appearing. Clear out a 16 by 16 by 16 room. This constitutes a chunk. Slimes won't start spawning immediately while you're here, but you may be able to force them to do so by adding platforms. Create four one-block high platforms. These platforms should be stacked on top of each other with three blocks of vertical space between each. Having these platforms increases the possible spawn area for slimes. Retreat at least 24 blocks away from the spawn area. As with the swamp biome, slimes won't spawn if you're 24 blocks (or closer) away from the spawn area. Wait for slimes to spawn. If you don't see any slimes within a standard night and day cycle, you'll need to find a new cave. 
Travel to a swamp biome. Find the flattest place possible. Enable your coordinates. Make sure the spawn area's Y coordinate is between 50 and 70. Find a dark spot. Make sure the spawn area has at least three blocks of vertical space. Retreat at least 24 blocks away from the spawn area. Wait for a full moon. Try to force the slimes to spawn. Search for caves below the 40th layer. Add torches to the cave. Clear out a 16 by 16 by 16 room. Create four one-block high platforms. Retreat at least 24 blocks away from the spawn area. Wait for slimes to spawn. 