A few things that helped the sailors travel these long journeys were the new technology. Compasses helped them along by showing them the direction they was heading in, Cartographers, or map markers made for more accurate maps and sea charts.

Ancient Greeks created what is called a astrolabe which was perfected by arabs, it determined the sailors latitude at sea.
New, bigger, and better ships were also built such as the caravel which was developed by the Portuguese, it combined the square sails of Europeans ships with arab triangular sails. It also had a sternpost rudder which made it easier to sail into the wind.