Rainfall in a tropical rainforest can be varied depending on the terrain, location of the rainforest and the time of year. It does not rain constantly in a rainforest and the sun does shine. Plants need both!
First, there is an increase in noise. Small frogs start to chirp and insects can become quite loud. They are responding to changes in barometric pressure as many of the creatures only breed during or just after a rain storm. Then usually the rain falls in brief, intense showers, lasting normally 5 to 15 minutes. It starts with a slight rattling on the canopy which grows to a loud roar that can be almost deafening. Mist will reach the floor at first as the rain water works it's way through the canopy plants, bouncing from leaf to leaf. Then as the rain continues, the upper leaves get saturated and heavy, eventually dumping onto the ones below and finally resulting in a shower of large drops that reaches the ground floor.
Ironically enough, if the rain continues the leaves become turgid, stiffening as the water pressure builds inside the plant and the rain will seem to lighten. Then the water gets channeled to the trunks of the trees and runs down them, so the rain seems to lessen even though one can still here it pounding down overhead. Then the shower suddenly stops and yet the water continues to trickle down as it moves through the lower canopy to finally reach the ground where it is absorbed.
Many of these showers occur during the night or early morning. The air is cooler then and can hold less moisture, so releases it as rain.
There are periods of prolonged rain, usually when major storm systems are moving through the area at specific times of years. In the Caribbean, this is during Hurricane Season (June through October) and in Asia it is referred to as the Monsoon Season. Then the rain lasts for several days and will be more steady, but still have the intense shower periods.
It is during these times that the floor of the rainforest becomes saturated and then rivers and streams start to fill and flow. This is important as the water will fill aquifers and lakes that are used by others. Those system's water will have been filtered and purified by the rainforest as it passed through.
After the shower, everything is fresh and clean. The sun comes out, creating a green glow as it filters through the now washed canopy. The birds start to sing and all of life is refreshed.