In general "класть" and "положить" are synonyms. There is a bit difference, I can`t explane it, but we more often use "положить". Difference betwen "положить" and "поставить" is a pretty big. "Положить" we use whis towel, robe, kind of food, pice of paper. We use "поставить" whis furniture, vase, glass. There is no rule about thise verbs, but we don`t use "поставить" whis soft object