Rain came in and was caught in the impluvium or cistern. Bedrooms were on the sides of the atrium. The fauces were highly decorated. In the garden or near the tablinum would be the lararium the shrine to the household gods. The garden was usually a practical vegetable garden, but sometimes was more elaborate.
Archaeologists can excavate the roots and tell what once grew there.
Also there are many paintings of gardens. There were protocols about who sat where. Because of the uniqueness of the site, some strange and unusual things have been found. Luxury goods are rare at archaeological sites, but an entire set of silver cups was found. Often silver gets melted down to make other things, but the owner of this set threw it down a well, probably believing that he'd be able to come back for it later.