This is a great question. There are many reasons why Abraham is considered a model of faith. Let me list three of them.
First, in Genesis 12, God tells Abram to leave his people and all that he knows to a foreign land. What does he do? He actually listens to God and trusts in his promises of blessings and goes. (Genesis 12:1-4) It is important to keep in mind that Abram does not really know where he is going.
Second, God promises to give him a son from his wife, Sarah. However, there is one problem. Sarah is much too old to have children. The text makes this point view clear in Genesis 15:1-6. Romans 4 in the New Testament is even stronger in it language, as Paul speaks of the "deadness" of Sarah's womb. It is clear from Genesis 15:6 that Abram believes that God can give him a son through Sarah and for this reason God calls him righteous. Later Abram's name is changed to Abraham (Genesis 17)
Third, after God gives Abraham a son, Isaac, God now tells him to offer his only son to him as a sacrifice. Abraham does the unthinkable; he is willing to offer his son to God in Genesis 22. God sees this and stops the sacrifice and calls Abraham a man of faith.