It really depends on where you were living. Lydia Maria Child, in her 1832 guide The Frugal Housewife, noted it was possible to preserve butter for a while:

if it be practicable, get a friend in the country to procure you a quantity of lard, butter, and eggs, at the time they are cheapest, to be put down for winter use. You {15}will be likely to get them cheaper and better than in the city market; but by all means put down your winter's stock. Lard requires no other care than to be kept in a dry, cool place. Butter is sweetest in September and June; because food is then plenty, and not rendered bitter by frost. Pack your butter in a clean, scalded firkin, cover it with strong brine, and spread a cloth all over the top, and it will keep good until the Jews get into Grand Isle [ i.e.forever]. If you happen to have a bit of salt-petre, dissolve it with the brine. Dairy-women say that butter comes more easily, and has a peculiar hardness and sweetness, if the cream is scalded and strained before it is used. The cream should stand down cellar over night, after being scalded, that it may get perfectly cold.

But if the average family of four had a cow, and it was milking, there'd usually be lots of milk. If it had a number chickens and they were laying, there'd be often lots of eggs. A spring house or root cellar was often cool enough to also serve as a place to store butter for a while, but if that wasn't available, dairy and eggs would be traded for other things. Child had a lot of recipes that required large quantities of milk, cream, butter, eggs- if the housewife was in the country. If she was in the city, sometimes the recipe is amended, so the quantities of eggs and dairy is smaller.

But if the cow was dry and the hens weren't laying, and the family couldn't trade for milk, butter, eggs, etc. then the cook might improvise. Like Indian Pudding:

Indian pudding should be boiled four or five hours. Sifted Indian meal and warm milk should be stirred together pretty stiff. A little salt, and two or three great spoonfuls of molasses, added; a spoonful of ginger, if you like that spice. Boil it in a tight covered pan, or a very thick cloth; if the water gets in, it will ruin it. Leave plenty of room; for Indian swells very much. The milk with which you mix it should be merely warm; if it be scalding, the pudding will break to pieces. Some people chop sweet suet fine, and warm in the milk; others warm thin slices of sweet apple to be stirred into the pudding. Water will answer instead of milk.

Lydia Maria Child :The Frugal Housewife

The European butter belt, where butter was the main fat used in cooking, lies in the north where heat wasn't much of a problem. The things that will turn butter rancid there are light and oxygen - protect the butter from those, and it can keep quite well. If it can be kept cool during summer (e.g., in a cellar), it can last quite long enough. When butter is your main cooking fat, you will tend to use it fairly quickly, and make or buy it fairly often, or get some out of long-term storage fairly often, so it doesn't need to keep for that long in the house.

The simplest way to protect butter from light and oxygen is to keep it in an opaque covered dish:

• https://commons.wikimedia.org/wiki/File:Butter_dish.jpg

This does expose it oxygen, but it limits the amount of oxygen near the butter. Depending on how quickly butter is used, a simple container will keep it fresh until it is used. For longer keeping, the French butter dish AKA butter bell AKA butter crock uses water to keep oxygen from the butter:

• https://commons.wikimedia.org/wiki/File:FrenchButterDishOpened.jpg

• https://i.pinimg.com/564x/4a/7c/21/4a7c21d1bccebbd2f0b24c7cc71692bc.jpg

These containers will keep butter fresh for a month at room temperature (i.e., northern European room temperature - I expect it would not work so well in Australian summers). I have read that this is a Medieval French invention, but cannot readily confirm this. Does anybody know?

These containers are suitable for the relatively small amount of butter in current use in the kitchen. To store larger amounts, a barrel can be packed full of butter (full, so no air is left inside) and sealed. Kept in a cool place, this will keep quite well. Low temperatures and cool temperatures can both be obtained by (a) submerging the barrel in a cool spring or (b) burying it in a bog. (Archaeological finds of "bog butter" are not all butter - some are dairy fat, but some are tallow.)

In warmer conditions, butterfat can be kept without refrigeration if turned into clarified butter (e.g., ghee), basically pure butterfat. In a sealed container, and protected from light, it will keep for a year or more. If the container has been opened (i.e., the butter in the container is being used), so that there is some exposure to oxygen, it will still keep for months. While the best-known clarified butter today is Indian ghee, there is also a European tradition of clarified butter, most notably in France where it is made from both sheep and cow butter.