There were two methods used to build the hulls of wooden ships, and each used different methods to make the hull water tight.

Clinker (or lapstrake) construction was used most famously by the Vikings, but also in later cogs and in many later smaller Northern European ships and boats. In this construction the planks or strakes of the hull are laid overlapping one another. This overlap gives a broad wood to wood joint. If the wood is shaped well by the builders, and clinched together well (generally by copper or iron rivets). The joint is very water tight.

Carvel construction comes from the Mediterranean. In this technique, the planks are laid butting up against one another. Here the wood to wood joint is narrower, and cannot be clinched together. Carvel ships rely on caulking the joints to make them water tight. Caulking involved using a scraper and hook to clean out the seam between the planks and then using a caulking mallet and caulking irons to pound and compress caulking (usually "oakum" which was tarred hemp cordage material) into the seam.

After caulking, the seams (indeed, the entire hull) would be covered with hot pitch (below the water line, often the caulked seams would be filled with paint or white lead above the water line). This was known as "paying" the hull.

http://www.sydnassloot.com/caulking.htm

Caulking did not last forever and hulls would need to have caulking repaired, or be re-caulked at intervals (10 years or so?)

None of these wooden shipbuilding techniques was perfect at keeping all water out. Ships took on water (especially when being twisted or "worked" by severe weather). Pumps (or bailers in the case of the Vikings) were employed to get excess water out.