During the Tudor period, cleanliness was maintained using linen undergarments. Washing with hot water on the body was considered dangerous, as the Tudors believed disease could enter the body via the pores.
Soaps and washing waters were used for hands and faces, with harsh lye based soap for the poor, and herb scented waters for the better off. Housewives often had their own recipes for these, and would keep them recorded in the house journal.

The preferred method was to rub the body down with dry body cloths, and then layers of linen worn on the skin, with their outer clothing on top. The linen worked to keep sweat and grease away from the skin, and could be changed frequently. The wealthier you were, the more linen you would have.

The Tudors also would use pomanders made of fragrant spices and scented oils, such as ambergris to smell pleasant. Tooth hygiene was patchier, with a combination of ashes rubbed on the teeth, cloth rubbing and picks being utilised. The rich often had worse teeth than the poor, as they would have eaten great quantities of sugar, and the poor could not afford to eat it.

So the Tudors were cleaner and much sweeter smelling than we give them credit for!.

Source: 'How to be a Tudor' by Ruth Goodman.
'The Tudor Housewife' by Alison Sim