Even today, most woman outside Europe/European Offshoots/Japan/Korea does not use commercial baby food or infant formula since they are prohibitively costly or cultural customs are present that does discourage it. My mom raised me without those, for example. In fact, the inverse is actually true. There is a constant encouragement toward breastfeeding for 2 years because organizations such like the WHO says it improves the immunity and digestion of the baby and is the main reason why most Europe has laws providing prolonged post-maternal paid leaves.

Anyway, a more historic answer: we know for many sources that before infant formula was a thing most wealthy mothers used wet nurses to breastfeed their babies so they didn't to do that work themselves (or if they had an issue pumping enough milk). Wet nurses were employers or slaves who had babies themselves recently (or they never stopped wet nursing after their last one). Most cultures did see this as acceptable, but they differed if it should be encouraged or discouraged, like in 18th century Europe were using wet nurses was discouraged (but tolerated).

For the common people, though, the mothers themselves had to breastfeed their own babies, and if the mother died or was sick or had issues pumping enough milk, the other mothers in her family would help or do the work altogether, or otherwise a female friend of the family. When no milking mother was available the fate of the baby was certainly bad, but that was a rare case since families were larger and more closely related back then or otherwise their community were there to assist them.

As for how long they breastfeed depends upon the local customs, but for example the Islam's Qur'an states the following:

Mothers may breastfeed their children two complete years for whoever wishes to complete the nursing ... And if you wish to have your children nursed by a substitute, there is no blame upon you as long as you give payment according to what is acceptable. (parts of Surat al-Baqarah 2:233)

And most the sources from other cultures also points out for similar durations, so we can say 2 years was held as the ideal even back then. Most mothers might have ended it earlier for time constraints (life was very busy for farmers), but at least they breastfeed 3 months since babies can't (at least properly) eat semi-solids before then, and I don't remember seeing a case of breastfeeding an adolescent neither (but yes pubescent kids).

During weaning babies ate semi solids like mashed rice or potatoes, alongside soups, tea and other liquids, until they became kids (near or during the second year) and able to eat solids. With that said, the nutrition of babies after weaning was often deficient, which was one of the many factors that contributed to the very high infant mortality rates that plagued all times before the modern era.

Source:

(2009) A History of Infant Feeding

Emily E Stevens, RN, FNP, WHNP, PhD, Thelma E Patrick, RN, PhD, and Rita Pickler, RN, PNP, PhD

It’s always hard to be certain of what typical practices are when the historical record focuses on the upper-classes, or, in the case of medical texts, is prescriptive rather than descriptive. There’s been isotope studies on medieval skeletons in an attempt to determine weaning age and childhood diet. I don't know much about the situation in Italy, but for the medieval British these seem to indicate weaning was complete by age 2 (Burt 2013). In the process of looking for that, I also came across this cool-looking study of dental wear in children in medieval Canterbury that found wear indicating soft foods in the diet in skeletons as young as 1. So far as what these soft weaning foods were, there is textual evidence for pap, gruel and panada, all of which amount to soft preparations of flour, grains or bread cooked in water, milk or broth.

If you’re interested in different child-rearing practices across cultures rather than just historically, you might like Lancy’s The Anthropology of Childhood, especially for a sampling of the sheer variety of practices found in the anthropological literature. Some simply feed whatever the adults are eating, which can cause illness in cultures that wean early. Others prepare special diets that might be more or less adequate than adult diets. In studying the Kpelle, agricultural people in Liberia, Lancy observed “mothers withhold the breast and force-feed infants rice water to accelerate weaning” (129), while the Hadza, hunter-gatherers in Tanzania, feed weaning children rendered zebra fat, bone marrow, and a gruel containing ground baobab seeds (Jeliffe et al. 1962:910 as cited in Lancy:107). It’s a fun read for feeling better about your own choices in the modern mommy wars.

• Burt, Nicole M. (2013). Stable isotope ratio analysis of breastfeeding and weaning practices of children from medieval Fishergate House York, UK. American Journal of Physical Anthropology, 152 (3) pp. 407-416. (paywall sadness)

• Jeliffe, D. B. et al. (1962). The children of Hadza hunters. Tropical Pediatrics 60(2):907-913.

• Lancy, David F. (2015). The Anthropology of Childhood: Cherubs, Chattel, Changelings. 2nd edition. Cambridge University Press.

• Mahoney, Patrick et al. (2016). Deciduous enamel 3D micro wear texture analysis as an indicator of childhood diet in medieval Canterbury, England. Journal of Archeological Science, 66, pp. 128-136.