So during the latter half of the 19th century, the American population became increasingly urban, but was still predominately rural. Food storage and preservation depended on individual resources and the urban-rural divide. For subsistence farmers, being able to store grain during the winter months was essential to survival (your crop wasn't just a source of food, but the thing you used to finance the purchase of non perishable goods like coffee, sugar, etc that were commercially available). By the latter half of the 19th century, however, industrialization also meant that regional agricultural specialization was increasingly viable. Canals, steamships, and railroads enabled faster transportation of goods, but did not neccessarily lead to increases in food preservation techniques. It wasn't until the early 20th century that industrial food preservation really took off.

Heat and moisture are the enemies of food preservation, so most preservation techniques involve drying the products and storing them in cool locations. Root cellars would've been where produce was stored to keep it fresh as long as possible. Meats would've been dried, smoked, or salted. Produce might've been pickled or fermented-- canning become more reliable by the late 19th century. The role of food preservation would've been the domain of women and domestic workers, and it would've been done within the household. With the exception of some dried and salted meats, preserving fresh produce was done in the home. The ability to do this was largely marked by class: the wealthier you were, the more varied your diet could be throughout the year. This applied both in urban and rural areas.

Enslaved persons (and later, sharecroppers) would've received food: generally a provision of salted pork and ground corn, but would've supplemented it with food they grew themselves in garden plots, which were separate from the land worked for cash crops. Barter (and market) economies supported the exchange and purchase of goods like eggs, dairy, and other meats to supplement what was provided and what could be grown. This diet was not entirely dissimilar from the diet of poor white farmers in the south, who also would've relied on supplementing a basic diet or corn and pork ( which were easy to store) with seasonally available produce and dairy, eggs, so on and so forth.

Wealthy (or at least wealthier) landowners would've have a much more elaborate system for food preservation, and there were often several purpose built buildings on property for food storage. In the north, ice houses were used to store ice (as much as was possible) throughout the year.Smokehouses would smoke meat, one of several preservation techniques to keep meat good longer. Grain houses might've been used to store livestock feed. The grain elevator, which enabled the large scale production and storage of grain as ways of regional transportation improved was invented in 1842.The industrial revolution essentially allowed for more regional specialization in agriculture, but certainly did not do away with localized storage methods in rural and agricultural communities, which tended to be more self contained.

Aside from what was seasonally grown and prepared by the household, there were also general stores in local areas that would've sold basic provisions like flour, coffee, sugar, dried fruits, dried nuts, some oils, maybe bacon and salt pork. These basics, coincidentally, were also the provisions purchased and used by those traveling out west (and when residing in the west), where farm land was generally less forgiving than in the south.

Food preservation in cities worked a bit differently, mostly because there was a more market system in place and you could generally buy goods from vendors throughout the year. Obviously, this system primarily benefited the wealthy who were able to buy high end and expensive goods, but even in the latter half of the 19th century as living standards declined, industrialized meatpacking industry also meant that meat was widely affordable. In the first half of the 19th century New York City, for example, there were meat, produce, fish vendors and grocers who sold goods within a public market system that operated throughout the city. This regulated setting eventually fell away, instead leading to a more disjointed privatized system. Without much in the way of industrialized food storage techniques, goods would've been brought to market as quickly as possible after being picked (or killed, in the case of meat), what I've read implies that preservation was largely the responsibility of the individual but in urban areas was even less common among the lower class, who could continue buying staples like bread or flour and meat throughout the year.

I hope this answers most of your question. When it comes down to it, there were definitely some straightforward preservation techniques, but they were used unevenly depending on where you lived, what was available, how it as available (did you grow it? did you buy it?), how much money you owned, whether you had hired help... so on and so forth.