When I look online it only describes how peasants "did" pickle much of their food, but not the containers they used. Did they use glass, barrels, ancient alien technology?
Ceramic jars of glazed earthenware or stoneware in some places, small wooden barrels in others, depending on the location and exact good being stored. With some pickled foods, there's no real need for a very tightly fitting lid. Less commonly, the lids could be sealed on with beeswax to form an airtight seal.
The cliche ceramic "honey jar" is representative of the general shape and deign commonly used for storing many kinds of non-perishable foodstuffs. Such types of ceramic jars are still widely used for traditional pickling in large parts of East Asia. Only in the 19th century did the proliferation of cheap glass jars with tightly fitting metal lids edge out the use of ceramic vessels for long-term food storage.
Many places would have also used small wooden barrels, depending on the local availability of suitable woods and the cost of fuel and so forth. Intent for trade is also a factor as wooden barrels are much lighter to transport any distance, but in many places ceramic vessels were cheaper and had the virtue of being more easily reusable.