How does deforestation lead to frequent floods and droughts? 

Trees help to make water vapour which is responsible for the rainfall. Cutting more trees will result in less rainfall because the process of making water vapour will slow down. Therefore. the level of groundwater will decrease and the ponds and lakes will start drying. Ultimately, this will result in drought.
Due to deforestation, the water holding capacity of the soil decreases. The roots of the trees get dried after they're cut down. The movement of water through trees into the soil slows down. The water of the rainfall collects on the surface which results in flood.