explore the areas that you normally find slimes in and you will find a baby slime that you can befriend (you must have at least returned from the snow mountains for the baby slime to appear)

For content

Stage 1 of slime development

There really isn't much to do you can choose to play or pet it. You can choose to feed it and the MC will feed it with cum (there isn't a scene just dialogue)

Stage 2 of slime development

If you explore some more you can find the pet slime again and if you have at least fed the slime I think 2-3 times during stage 1 the slime will appear more grown. If you have 40 or more lust you can "feed" it (have sex with it) unlocking the first sex scene

Stage 3 of slime development

After you "feed" the pet slime 3 times during stage 2 (having sex with the slime removes 10 corruption) it shall grow bigger once you meet it again. If you have 40 or more lust you can "feed" it unlocking the second sex scene

Final Stage of slime development

After you "feed" the pet slime 3 times during stage 3 it shall grow even bigger once you meet it again. If you have 40 or more lust you can "feed" it unlocking the third and final sex scene.

hope this helps