Get a camera rain cover. They come in all sizes, and prices start from a few dollars. The more advanced ones have more functions like higher visibility and better ergonomics, but they are still on the cheap side.
Carry a plastic bag. When in lack of better options do not minimize the importance of such a basic object. It can help you achieve that sought-after shot and protect your camera while doing so. Just punch a hole in it big enough to fit the lens and be sure that the top plate of the camera is also covered by the bag. Stick your hands in there and you're good to go. Elastic bands help secure the bag on the camera.
And a UV filter attached to the lens will prevent exposure to water. Pay special attention to zoom lenses. Due to the lens moving when changing focal length, water can infiltrate unnoticed.
Of essential importance is also having a soft cloth. You will keep it dry and tucked away in a pocket in case water gets on your camera which is almost inevitable.