Indigenous North American cultures as well as some South American cultures and the Sami people of Scandinavia relied (and in some cultures still rely) on cradleboards to transport and contain the infant. These vary by culture, but are essentially carefully-shaped, decorated, wood-and-leather-and-plant-material baby backpacks that the mother carries with chest or head or shoulder straps, depending on the region. Many have a wooden arch near where the baby’s head is to be a “bumper” and prevent stuff from colliding with baby, and to allow dangly mobile-like toys to be tied. South American indigenous cultures often use cloth or leather pouches similarly.

With use of the cradleboard, the mum can secure the baby within, and carry baby with her to get her work done or travel. Mum would then have two free hands/arms. The board could also be taken off and propped/leaned against a tree or structure if mum needed less burden. Baby would be cozy and contained so it could not wander off into danger, or towards a fire. Some cultures especially valued the quiet observation baby would have during this cradleboarded infancy, learning about the world and developing patience during this period. Babies would be taken out of the board at certain daily points of course. And as they grew older, they’d spend more and more time out of the board.

Also notable historically, some indigenous groups used specific cradleboard head-straps or wraps for babies that would be tight enough to influence the shape of the skull in a way that group thought was beautiful and identifying. The Choctaw and Chehalis are North American practitioner examples. Mayans and Incas also practiced artificial cranial shaping with headwraps (not necessarily affixed to cradleboards).

I can try to make a bit of an answer for France and a bit of G-Britain/Spain/Italy in the XVI-XVIIIthe century.

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Tho one thing to remember is that all the things i'm about to list varied very much from a place to another. My knowledge of this subject mostly comes from Stéphane Minvielle's "La famille en France à l'époque moderne", who himself refers a lot to Phillipe Ariès's work if you want to dig on this subject (i think part of it was translated in English), Jean Louis Flandrin did some things on childhood too, but not sure it was translated.

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- For babies specificaly, they were expected to die early (around 1 out of 3 died in the first year) so the first concern was to get them baptized. Because if they weren't and died before they would not go to Heaven.

-The baptism was also the occasion to do various, (more or less inherited from the pagans) rituals, varying from a place to one another, for instance, according to XVIIIth century folks if you rolled your kid on the altar it would prevent limping. Other things like putting a coin in the baby's clothes would bless him with great wealth.

- For feeding, babies would usualy eat breastmilk. In the case of babies sent to nurses (which represented LAAAAARGE amounts of babies in the XVIIIth century -close to half of them in 1750 in Paris-, not as many before), sometimes the nurses would feed them milk cow, which was an additionnal cause of bad health for the babies if it hadn't been treated correctly before.

-for clothing, the baby would keep the same "swaddle" (not sure of the word, like pieces of rags you dress a baby with) for the first weeks or months of his life, which wasn't so good for him too you can guess.

- During the day if they weren't sent to a nurse, they would usualy either be taken care of by an other inhabitants of the house (i.e a grandmother), else they would just go with their moms. This was facilitated by the fact that before the very late XVIIIth century people would usualy work either at home or in the fields near their home. Later they would either be sent to school, or (more often, since school only really developped in the XVIIth-XVIIIth century) be left alone with the other kids, at the age of 7 they would start doing some smallworks too (keeping a few sheep for instance), learning of an actual craft would start around 9/10 years. If you want examples about a peasant's childhood maybe check the biography of Valentin Jamerey Duval, he was a commoner that became librarian for the counts of Lorrain, so he wrote his mémoires were he speaks about his childhood, for a more urban one check Jacques Louis Menetrat, a glassmaker who wrote a journal of his life.

-For babies's bedtime i don't really know. One thing is that people usualy rarely had more than one or two beds in the house, so kids very often slept with their parents (especialy pre XVIIIth century) and small children dying after getting crushed by a sleeping parent were a common accident. Also i have seen accounts of the parents reading the bible to kids before sleeping (for instance in Nicolas Restif de la Bretonne, a small countryside French Nobleman) but im not sure how common it was. Prayers before sleep were also a thing back then.

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Hope it answered partly, if you have any specific questions feel free to ask.

/u/Antiquarianism and /u/Freevoulous and /u/-Baobo- have previously answered How the heck did people survive in prehistoric times when they had babies?

Others might have original answers for you.