This varies greatly between cats, with many cats managing perfectly well without any intervention at all. For those who need a little help, a good rule of thumb is that short-haired cats can benefit from a weekly brush; with long and medium haired cats being brushed ideally every day or two.
Bathing is usually not necessary for healthy cats unless advised by a vet for treatment of a skin problem; or to remove potentially toxic substances from the fur. This is fortunate as most cats do not enjoy being bathed and can become quite agitated.
If you do need to bath your cat, it is helpful to put a rubber mat at the bottom of the sink or tub to help your cat keep their footing and feel less out of control. The water level should also not be deep, but rather poured over your cat gently with a cup, avoiding the eyes, ears and nose. Use only shampoos that are registered for use in cats, as other shampoos may be of the wrong pH or contain ingredients that are not safe for cats. Cats will want to groom themselves after a bath so thorough rinsing is necessary to avoid them ingesting the shampoo.