well everybody knows how its starts, it just simply starts when it first the sky will get dark or it will get cloudy then starts falling a little bit of drops of rain slowly then it gets faster and faster. that's how rain starts.
Rainbows occur when sunlight passes through drops of water. This is why you see rainbows after rain or at fountains and waterfalls. Light moves at different velocities through air and through water. So when sunlight passes through water, it is dispersed. It is first refracted when it enters the droplet, reflected of the back of the drop, and then it is refracted again as it leaves. This refraction of the light into angles within the drop leads to it being visible, and the wavelength of the light is what depends its colour.
After rain when sky is clear from the clouds and there is water everywhere. The sun shines on this water and reflects on the sky as rainbow.