I said this many times before that electricity and water do not get along. Nevertheless, sometimes it just rains when it is not supposed to. When I was in Hong Kong July 2017 the weather was really bad, it just kept raining and raining. This would be my first advice: Just wait until it stops raining.
Umbrella
Get yourself an umbrella that will cover the camera. You will work after you were wet, I am not so sure about your camera.
Team up
Look for somebody to hold the umbrella while you manipulate / set up the camera and your equipment. After you took the shot, swap it so the other person can take a photo.
Location
If you cannot team up, look for a location to shoot from shelter. Like the photo above. I was standing under a bridge and had enough time and I was not in a rush to set up my camera.
Camera and Equipment Bags
Most essential is that your camera and lenses stay dry! Make sure that your bags are water proof. Even if the rain stops, the floor might still be wet! (Just in case you want to put your bag to the ground…)
Since I do not trust all the photo-bag manufactures, I always have a plastic bag on me so I can throw everything in there, like the camera, the lenses, cell phone etc.
Benefits to take photos in the rain
Yeah, I know, you heard this before: Rain causes beautiful reflections. The water reflects all the light and this increases the photos nice look.
Rain is sort of a magician, it lets people disappear! Most of the time when it rains, I did not have to wait for people to disappear, they just never show up.
Last but not least
Dry of your Photo-Bag at home! If it was exposed in heavy rain, it also needs proper drying – otherwise there will be fungi everywhere.