Luckily, we have the diary of Columbus' fist navigation, thanks to a diligent copy inserted by friar Bartolomé de las Casas in his Historia de las Indias.

Columbus started his journey going for the Canary Islands, as there he could have the last repair done to his ships, and he could get some extra supplies, most notably water, which is the most important thing to carry for a long journey. From Palos to the Canary Islands, the journey, according to Columbus' diary was quite straightforward, some days not even noting down the mileage or the direction, as going to the Canary Islands was not something exactly unknown.

Finally, on September the 8th, he started his journey across the Atlantic due West, as stated on the log: At three hours in the night the wind started blowing NE, and the Admiral took his way and route due West. The sea was very strong at his prow, which encumbered his voyage, and that day with its night he sailed 9 leagues (note: 36 miles)

The rest of the voyage, he continued going West, with the occasional correction as the ships were led a bit astray by the currents and winds, so the navigation had to be straightened in order to keep the proper direction. The general direction did not change until October the 8th, when the route starts pointing SW instead of due W. These are the directions stated on the diary from that day:

October 8th: WSW, about 11.5 or 12 leagues.

October 9th: SW, 5 leagues. W, a quarter NW 4 leagues. With the night hours, total distance of 20.5 leagues.

October 10th: WSW, with the night they sailed 59 leagues.

October 11th: WSW, 27 leagues. At night, due W, 22.5 leagues.

Columbus' idea was to sail due West from the Canary Islands, and in that direction he should get to the Isles of Spices, also known as the Oriental Indies.