The application of a light layer of oil is an excellent means to keep brassware shiny. Mineral oil and linseed are both good options to use for the prevention of tarnishing.
To apply the oil, simply pour a small amount onto a dry, soft cloth and wipe a light, even coat onto your brass fittings and fixtures.
For a better insight, take a look at our dedicated blog on the subject, Bathroom Brassware: The Complete Care Guide.