How were the people of the Old Testament saved?

This is a question that comes up sometimes in Sunday school or in small groups as the conversation somehow leads to the ideas of the Old Testament and how the people came to a saving knowledge of Christ. Does it make a difference that Christ had no yet took on flesh and dwelt among us? If there is no other name under heaven by which men are saved, then how did these Old Testament figures come to be "saved" as we understand it today? There are so many instances in Scripture that answer this question, whether directly or indirectly, but I will just point out one particular verse that might help to understand this concept of how Old Testament "believers" came to a knowledge of Christ. It comes from the great "faith chapter" in Hebrews. After mentioning the faith of Abel, Enoch, Noah, Abraham, and Sarah, the author says this:

These all died in faith, not having received the things promised, but having seen them and greeted them from afar, and having acknowledged that they were strangers and exiles on the earth. - (Hebrews 11:13)

Faith is not something abstract in the Bible - when it is mentioned, it is not used in the same context as people use it today, i.e. "believing in something." Having faith in the Bible is believing in one particular Person - the very Object of all of God's promises. Paul says in 2 Corinthians 1:20 that "all the promises of God find their Yes in [Christ]." Having made this connection then, there is something about the nature and foresight of the Old Testament saints that allowed them to greet the prospect of Christ in all of God's promises "from afar." They saw in God's promises of redemption, reconciliation, and eschatological consummation a single figure in the future that would bring all these things to pass. They saw the figure of the incarnate Son of God...and they believed. They all "died in faith," believing that God would accomplish his promises in Him.