Every place has its own charm during rainy season, therefore, for good photo opportunities travel around to catch different places and scenes. Make rain photography a part of the overall fun, not an end in itself by feeling free to venture out.
Serious hobbyists take several shots of the same subject, trying different angles and exposures. Note the location, time of day, lens used, aperture and shutter speed as soon as you take the photograph. Experimentation is essential for moving towards better shots during rainy season.
Monsoons present umpteen opportunities for photographing both events and the nature. The nature during monsoon looks beautiful due to striking colours and sharpness. Rainy season conveys a soft mood. And you may like to experiment with Black/White or Sepia mode for a few shots, if the camera permits.
The inset collage of photos illustrates some situational examples of rainy season photography. You may like to begin with some shots of this kind and then move on to better shots to capture the events and situations during rainy season.