Genuine Pearls have to be separated from your regular jewellery. Because the pearl itself is soft and can scratch very easily. Therefore, you want to store your pearls in separate soft cloth drawstring bags (which I prefer) or wrap them separate in a soft cloth, which then you can put in your jewellery box with your other jewellery.
When cleaning your pearls, all you have to do is use a soft cloth and gently polish them or you can buy a special jewellery cleaner for delicate gems which includes pearls. But do not leave your pearls in the cleaner for long. I found that 10 seconds or less is good enough, rinse them, polish them gently and they will be like new again.