All jewelry should be taken off prior to any contact with water, chemicals or any other substance that may come in contact with your new jewelry. This is especially important when the stones are natural and not stabilized. This will help with any potential damage to your new jewelry.
All natural stones are porous. Limit being around oils and soaps. This can discolor the stones as well as exposure to pools, or baths.. It is recommended not to expose natural stones to these as they can permanently discolor it.
Many of the jewelry pieces come with a certain finish or patina. These can be cleaned if needed to with a soft cowhide cloth. Jewelry with these finishes should not be soaked in a jewelry cleaner. They also can be cleaned professionally with your jeweler.