One claim that lazy cyclists from sunny countries affirm is stop cycling when raining, even if it drizzles. Though you should pay extra attention to the road and bike lines because of falling in curves when raining, it is not impossible to do it. Indeed, riders from rainy countries even enjoy and appreciate it. It is just a matter of mentality and use the appropriate garments.
Habitual clothes to deal with rain when cycling range from raincoat (better if it is long and allows you to pedal without problems) to waterproof trousers, boots or gloves. Waterproof garments have boomed partially because of the sportstores specialization in urban cycling as well as its resurgence in the last decades. Moreover, research in new materials has helped it.
On the other hand, some cyclists use umbrellas when raining. It is probably uncomfortable, specially to those who are not used to it, but could be effective with absent wind. Here you have an example:
Going a step further, some brands have developed a modified bike to incorporate a kind of umbrella which also protects from headwind:
And finally, other firms have put on the market something in between the two previous examples:
In this case, the biker should wear at least waterproof gloves and raincoat.