I'm in Old Testament I this semester -- what a fantastic blessing, since I've often struggled with understanding how to apply the OT to my life, or even how to read it faithfully. So how do you do this? Spurgeon said it in regards to preaching, but I think it applies to reading scripture as well. Place it properly in the big picture, and then "make a beeline to the cross."
I've found the following questions helpful (examples from my morning reading [Leviticus 10-18] in parentheses):
1. How does this section of Scripture fit into God's plan to redeem for Himself a people? (Israel is out of Egypt! Now God is shaping them into a people who will stand out from those around them. He is concerned with every detail of their lives -- what they eat, what they wear, their sex lives, their friendships, etc. -- and provides guidance for each step. He also gives them a system to deal with sin.)
2. How does this section of Scripture point to Christ? (Emphasizes the need for Christ! The blood of an animal cannot fully atone for the sins of people. Also emphasizes God's grace in dealing with His people despite their sinfulness, and His forbearance in forgiving them until the time for the Messiah is fulfilled. There are also pictures of Christ: the sacrificial lamb, the intercession of the High Priest, etc., as well as reminders of the life of Christ: Mary and Joseph followed these very guidelines when they brought Jesus to the temple.)
3. What does this section of Scripture say about the Character of God? (He cares for His people in the direst of circumstances, and no detail is too small for His personal direction and care. He is a God of truth and clarity! He will not go back on His word -- He will carry out His promises to His people, and will keep the terms of the covenant even when His people fail.)
4. What element of this section of Scripture can I cherish today as I meditate on God's word? (God's faithfulness! I have been incorporated into God's promises, because I am part of God's people! Christ kept the law for me, since I could not, so my salvation does not depend on holding to these ceremonial laws.)
These questions have been so helpful as I read the "boring" parts of the OT. As Christians, we read all of Scripture in light of its climactic event: the incarnation of Christ.