With some microphones it is quite easy to unscrew the microphone grille. This allows for thorough cleaning using a brush and soapy water. If the microphone grille cannot be removed, the surface can be cleaned with a cloth using a disinfectant agent (please make sure that the cloth is not too wet).
If the microphone grille cannot be removed, a hoover should never be used for cleaning, as this can destroy the fine mechanics in the microphone.