Like for riding in the wind, riding in the rain calls for caution.
Braking has to be estimated in advance and not left to the last minute.
The rims on the wheels are wet so the brake pads are not as effective so longer distance is needed for an effective stop.
One thing to be aware of is that while the rims are wet, the brake pads will shed water off them as they press into them. This could lead to the breaks suddenly finding a dry patch and resulting in a sudden stop (I have experience a lovely summersault down a hill in the past). So longer braking distance allows for a more gentle pressing of the pads on the rims.
Cornering is another part of riding in the rain which needs attention. Diesel reacts with water and gets displaced, resulting in bigger oily patches on the surface. So it's best to slow right down and keep the bike as straight as possible when turning.
Painted lines are to be avoided completely as these are sure to make the bike slip.
Metal man-holes and drain covers could cause problems and should be cleared well in advance. If it is unavoidable these are better taken straight and in the middle, without trying to turn on them or just before them.
Overshoes help keeping the feet fairly dry. If the shoes get drenched however the best thing is to fill them with newspaper pages, keep them inside for three or four hours at least; this soaks up the humidity and the shoes are ready to be used the next morning or at the end of the working shift.
A peaked cap is also good to protect from incessant drops and keep visibility to an acceptable level.