The hidden card

[I learned about this problem from Lyle Ramshaw. See also puzzles 19 and 20 on the following large collection of mathematical puzzles.]

In this problem, you and a partner are to come up with a scheme for communicating the value of a hidden card. The game is played as follows:

Question: What is the foolproof scheme that you and your partner settled on ahead of time?

As a follow-up question, consider the same problem but with a 124-card deck.