Genesis 24

The Text
Verses 1-9 - Abraham sends his servant back to Haran to get a wife for Isaac.
Verses 10-14 - the servant prays for God's provision in this mission.
Verses 15-28 - God answers as Rebekah meets him and waters his camels.
Verses 29-61 - Her family meets him and he explains.  They and she approve.
Verses 62-66 - Rebekah meets and marries Isaac.

Christ in the Text
The connection is a bit symbolic, but also a central theme of Scripture:
God arranges a marriage, providing a bride for His Son. 
Abraham is in the role of God.
Isaac in the role of Jesus.
Rebekah in the role of the Church.
This chapter is a blurry picture of Christ, though, because when God works to get Jesus' bride in history, He sends His Son Himself, not a servant.  In Genesis 24, Isaac just sits and waits.  Jesus sacrifices and lays down His life for the Church.
Ways the picture works:
Abraham like God has foresight and resources and acts according to God's promises to bless Abraham with offspring.
Isaac like Jesus is blessed and delighted to receive His bride (John 17:24).
Rebekah like the church is willing to devote the rest of her life to a Husband she has never seen, trusting God that He is blessing and fulfilling promises to His family and to herself as she becomes part of it.

Doctrinal Understanding
This is the middle and longest chapter of Genesis.  Moses could have told the story with a lot fewer words, but draws it out, both for literary drama and for emphasis on the importance of a bride to fulfill God's promises.

Cultural and Personal Application
To carry on the Christ centered metaphor, as Rebekah is willing to leave her family and identify with another one publicly, so must Christians decide to live according to different "house rules."  The church should submit to Isaac's (Christ's) headship, not to deceitful Laban's.  Rebekah and her family didn't always do this so well (Genesis 31:32; 35:2), and neither does the church - often tempted as we are to compromise with and identify with the world instead of our Savior and Bridegroom.