Apparently the basic outline of tooth care has not changed overmuch in the last 300 years, at least in English-speaking cultures.
Ask the Past quotes Thomas Raynalde in The Byrth of Mankinde with dental advice to seek the help of a professional for a thorough cleaning, although he recommends "a Barber" to "scoure, rubbe, and picke them cleane, and white." Dentists were yet to be known. Regular care of teeth in between visits is advised, especially to "picke them cleane that no meate remaine and putrifie betweene the teeth." Nothing turns off a social encounter like having meate putrifie in your mouth.
Whitening could be achieved by grinding white river pebbles into a fine powder and mixing an ounce of that with a "dramme of Masticke," or sticky plant resin. Apply this to the teeth to keep them "fayre and white," but "beware yee touch not, ne vexe the gummes therewithall."
Because even fayre and white teeth can't help you if you've got vexed gums.