The answer over that period varies quite a bit, because ships of the 1400s did not tend to go on extended voyages nearly at the rate that ships of the 1800s did. But it's an interesting question/answer, because solving the problem of supply is one of the reasons why navies (and British navy in particular) were able to more effectively project power at sea over time.

So, as an overall caveat, you have to keep in mind that most voyages of the time weren't simply sailing across the ocean for weeks on end. Navies were generally attempting to interdict a port, fleet or spot near land, and merchant ships were trying to get from one place to another and often stopping frequently.

In terms of the "how did they provide enough fresh water and food" part of the question, the answer is basically that ships and fleets did two things:

1. pack huge amounts of preserved food and tons (literally, tons) of fresh water into their holds;

2. stop off at friendly ports and buy fresh locally, and re-water from creeks and rivers.

In terms of what they would be provisioned with: the daily ration changed over time, but bread (in the form of hardtack); salt meat (pork or beef), dried vegetables (often peas) and dried fruit (raisins/currants) would be the basic ration. There were also other long-lasting foods, like portable soup (think dried soup that would be re-watered) for invalids. In the British navy, beer was served in home waters, as well as wine/arrack or rum overseas, depending on the station and the time period you're interested in. But the beer or liquor ration wouldn't provide enough liquid for a working day, so we know sailors drank water throughout the day. Most of the ship's water, though, would be used to soak the salt meat before cooking.

The ship often also carried a small manger of goats to produce fresh milk and chickens for eggs, but those delicacies were usually reserved for the officers. The officers' mess would also pitch in money to have more fresh or more delicate stores (jams, potted meats, pickled vegetables) available, but that was by private subscription and when it ran out they ate the same food as the men. Fishing could supplement this, as could catching turtles or local fauna, but was never (except in emergencies) the main source of provisions.

You also might be interested in this thread, to which /u/davidaop and I both contributed, about problems of supplies more generally.