In Minecraft, you can find slimes in two different ways.

One way is the special “slime chunk”, a 16×16 block area, where slimes spawn below layer 40. Many people use this to generate mob farms. Open your eyes when mining underground to find some slimes, especially on full moon.

There is another way to find slimes and this happens in swamp biomes. Here you can get an overview of all the areas with a swamp biome.