Health & Hygiene

"Aemilia smiled at her two friends as she approached. Her own attendants joined the group that trailed behind the two women, letting them walk ahead of their own volition for a bit of privacy. As nice as the day was, the hot sun was still beating down, and Aemilia could feel beads of sweat forming on her forehead. In a few minutes, the three women decided that a trip to the baths next door was in order. The majority of the day was given over to the men at the baths, but the morning was free for the women to relax and clean themselves. 
"Handing over a small fee at the door, the women walked in. They first stopped off at the cloak room, allowing their servants to help them remove their clothing. Next, they took a dip in the cold swimming pool, a refreshing change from the heat of the sun.
"The warm pool next was a shock to their senses, but they soon warmed up, wading in the small pool. Then came the hot room, where they sat in the heat, letting themselves sweat. After all of this, their assistants came and rubbed them down with olive oil to exfoliate the skin. Aemilia took up a strigil and scraped off the oil and the grime that went with it. A nearby stylist fixed up her hair, which had come loose from its curls in the baths, as well as retouched her makeup. The morning had gone by quickly, and Aemilia waved a goodbye to her friends, ready to head home."

The rich of Imperial Rome were the lucky ones when it came to health and hygiene. Where a poor family would have to use public restrooms and drink water from fountains, the wealthy had access to private facilities and running water. Cleanliness was a meaningful symbol for the Romans, especially the upper-class, and so they behaved as such, indulging in the experience of cleaning their bodies. Baths were taken daily, especially when a feast was happening that night.
Soap was discovered, by way of the Germans, in the 1st century AD. However, soap was mainly used to clean clothes, a relief from the past practice of using distilled urine. For cleaning oneself, though, the common practice was using olive oil and a strigil to exfoliate the skin.

Toilet-set, consisting of two strigils and an aryballos, 1st-2nd century AD. Courtesy of www.britishmuseum.org. Read more about it here.

Though this specific set belonged to an athlete, it's a good representation of what the bath tools of the day looked like. The aryballos is an oil flask that would have been filled with olive oil and then poured over and massaged onto the body. After that, the user (or their servants) would have taken the strigils and scraped them down, taking off the oil and exfoliating the skin. As painful as that may sound, it was a healthy practice, and exfoliants are commonly used today, if not in the same manner.
A typical bath house consisted of a collection of rooms and pools, each with a different purpose. At the entrance sat an apodyterian, or cloakroom, where clothes were left before continuing to the pools. The next pool was a frigidarium, a cold swimming pool, and a tepidarium, a heated room that contained a small pool. There was also a caldarium, which was a hot room with a bathing pool. Akin to a modern-day sauna, this room caused its occupants to sweat. Next the caldarium may have been an even hotter room called the laconicum, but it was not used by most.

Medicine and health, however, was another matter. 

Childbirth in ancient Rome: the birthing chair and midwife. From Tomb of Scribonia Attice, Ostia, Italy. Terracotta. 2nd c CE. Photo courtesy of travelswithnancy.com.

A large percentage of children died very young, or even in childbirth, as well as their mothers. Most mothers were very young, as the Romans believed that it was safer the younger the mother was. Births were typically assisted by midwives, who helped the mother through the labor and brought the child to its father after it was born.

SOURCES:

http://www.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=399791&partId=1
https://www.thoughtco.com/hygiene-in-ancient-rome-and-baths-119136
Usborne Internet-Linked Romans by Anthony Marks and Graham Tingay, pages 60-61 & 68-69
http://www.pbs.org/empires/romans/empire/family.html
http://travelswithnancy.com/women-ancient-rome/motherhood.htm