In the 16th century, the biggest problem wasn't finding your way on land, where there were usually distinguishing features (unless you were Hansel and Gretel). And for another thing, unless you were heading into uncharted territories, there were maps.
|(16th-century map of London)|
Besides, even if you were headed into parts unknown, on land you could use an astrolabe - a device first developed in the ancient Muslim world - to determine your latitudinal location through the positions of the heavenly bodies. But on the high seas, one wave looks pretty much like another, and the pitching and tossing of a ship made astrolabes unreliable. And as it happened, exploration by sea was the name of the game in 1500's Europe, and so it was urgent that your country find ways to get your ship to the New World before another country got its ships there first.
Magnetic compasses were in widespread use by then, and so you could always generally determine the direction in which your ship was headed. Mariner's astrolabes - made of brass and much sturdier and heavier than regular land-base astrolabes - were known of by the time of Columbus's voyages, but were too rudimentary to be very useful until 16th-century Portuguese explorers redesigned and improved them. The new mariner's astrolabes enabled sailors to determine their latitude by measuring the angle between the horizon and the North Star. And because the North Star is often obscured by clouds or fog, and is below the viewer's horizon in the southern hemi-sphere, sailors learned to use the sun as an alternative point for measurement.
But 16th-century mariners could not calculate longitude, because that required comparing local time with the time at a distant location, as determined by a clock, and 16th-century mechanical timepieces were not accurate enough to afford that kind of precision. So instead, navigators used a system called "dead reckoning," which essentially consisted of educated guesswork. Starting at a known position, the navigator would make his best estimate of the heading and speed of the ship and the speed of the ocean currents. Time was determined by very careful onboard monitoring of hourglasses, and speed was determined by throwing one end of a weighted rope, knotted at regular intervals, overboard, and then counting how many of the knots passed through a sailor's fingers during the running of a one-minute hourglass (which is why nautical miles per hour are still called "knots").
These methods might not sound like much, but, as they say, the proof is in the pudding. Before the year 1600, both Ferdinand Magellan (in 1519-22) and Sir Francis Drake (in 1577-80) had circum-navigated the globe.
Crew of Willem Barentsz fighting a polar bear in the Arctic (1596)