Columbus wasn't at sea for "months." He left the Canaries on Sept. 6 and sighted land in the Americas on Oct. 12, at which point he would have been able to find fresh water on land.

That said, he kept water for his crew the same way other sailors of the day did: in wooden barrels, filled before he left from springs, streams or rivers that were known to be good sources of fresh water. They could supplement that water with fresh water gathered in storms, and a normal function of any navigator was to take note of places where the ship could be re-watered and re-wooded (to be able to light galley fires).

Most water -- probably 90 percent or so -- on men-of-war of this era would in any case be used for soaking salt meat to make it palatable.

By the end of the era I'm familiar with, RN ships were experimenting with storing water in iron tanks, rather than wooden casks, but the wooden barrel was the basic medium of water storage throughout the period.