One of the easiest ways to keep your cockatiel healthy, is to keep his cage clean.  This involves changing the newspaper (or lining) at the bottom of the cage every other day, changing and cleaning out the food dish every day, and changing and cleaning out the water dish every day.  Perches should be scraped clean whenever they become soiled.

Do not keep your bird in extreme cold or heat.  Make sure your cockatiel doesn't freeze to death if you keep it by a window.  If your cockatiel shows cold symptoms, make sure you call your vet.  Birds can not catch the human common cold or flu, but humans are capable on contracting many bird diseases.  Make sure you wash your hands before eating.

Please take a look at the toxic plant list prepared by the NCS.  In addition to the items on the list, never give your cockatiel chocolate, avocado, or expose it to teflon fumes (which means don't cook with your cockatiel on you).