|"My scheme is intended only for honest men."|
A quick bit of history. The man credited with inventing the Borda count is Jean-Charles de Borda. He invented a lot of things and has a crater on the moon named after him.
How the Borda count works
The Borda count is really simple. Suppose 5 candidates are running in the election. The voters rank the candidates, and each candidate gets 4 points for every first choice, 3 points for every second choice, 2 points for every third choice, 1 point for every fourth choice, and no points for last choices. You count up the points, and the person with the most points wins.
Sometimes you will see other point systems. E.g., 5 points for a first choice and 1 point for a last choice. Sometimes it is reversed and you get 1 point for a first choice, 5 points for a last choice vote, and the person with the fewest points wins. You get the same winner either way so it doesn't matter.