While (much) more can always be said, I summarized how people dealt with the cod to be preserved in pre-modern times before in: How did the people of the past dry and store fish and other foods?

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1. Salted
2. Dried
3. (Smoked - mainly in smaller scale than former two? )

These threefold are the main way to preserve the fish, though which one preferred also depends on the kind of fish, climate conditions of the locality and access to salt.

Did they put them in barrels?

As I mentioned just recently in: What was the true extent of Hanseatic trade control in Europe?, medieval Hanseatic merchants exported salted herrings originally caught off the Scanian coast (now in Sweden, then in Denmark) and put in barrels, though they mainly cured caught fish on land, not on board of the ship. Some kind of barrel or casket was also employed onboard to store fish up to their cure.

It was not until late medieval (after about 1400) or early modern period that fishermen began to cure fish (herring) on board, and the Dutch fishermen probably employed this method first (Unger 1980: 257). A scholar (either de Vries or van der Woude calculates that about half a million barrels were used by the dutch fishermen in Dutch herring fishery in the 17th century.

(Added): Recommended Reading (Classic on the topic):

• Braudel, Fernand. Capitalism and Material Life, 1400-1800. trans. Miriam Kochan. London: Harper Collins, 1973.
• de Fries, Jan & Ad van Woude. The First Modern Economy: Success, Failure, and Perseverance of Dutch Economy, 1500-1815. Cambridge: Cambridge UP, 1997, especially Chapter 7.

Add. Reference:

• Unger, Richard W. “Dutch Herring, Technology, and International Trade in the Seventeenth Century.” The Journal of Economic History 40, no. 2 (1980): 253–80. http://www.jstor.org/stable/2120179.