The answer to 'how to maintain bathtub' is to regularly clean and inspect your bathtub to keep it in good condition. This includes scrubbing the tub surface, unclogging the drain, and checking for any cracks or damage.
Start by giving the tub a thorough cleaning with a mild abrasive cleaner and a soft sponge or cloth. This will remove soap scum, hard water stains, and other buildup. Be sure to clean the drain cover and overflow drain as well. Rinse the tub thoroughly when finished. You should clean the tub at least once a month, or more often if it sees heavy use.