How was the vice president selected under the original voting system?

Under the original system, however many candidates would run for president.  The electoral college would vote on the candidates.  Each elector would vote for two people.  After the electoral college had done its vote, whichever candidate got the most votes would be the president.

Unlike today, however, the candidates would not have vice presidential candidates already picked.  Instead, whoever got the second most votes would become the vice president.  This was a bad system because, as it turned out, you could get presidents and vice presidents who were political rivals, as when Aaron Burr became Thomas Jefferson's vice president.