When you save your leaderboard, you will receive triggers for Storyline/Captivate that are needed to save data to the leaderboard. It really doesn't care whether your number is time (seconds?) or anything else as long as it's numeric.

I'm not sure if I'm following. I need to know how to add time stamp the user took to complete the quiz. I am planning to use a count up and not the count down option. So basically the user with the quickest and highest score should appear on top.

The leaderboard does not have either count up or count down options. If you're saying that you will use the timer widget and also the leaderboard, and want to the variable from the timer widget to be recorded in the leaderboard instead of the score: when setting up the leaderboard there's a text entry field (variable name for the numeric field) - whatever variable you give it there, that's what will be recorded. If you give it a variable you set up for the timer then this variable will be recorded in the score column.