Leviticus tells a story, a story of what is pleasing to the LORD. Not so much through action but through sacrifice and community life.
It sings the song that Hebrews laments, priests never at rest but always offering sacrifices for sin. The only way to life is through death - the human race cannot be reformed it must be condemned to death and then resurrected. The flesh can't try harder, new life must come through the Spirit.
The book picks up where Exodus leaves off - the LORD has made his dwelling with his people in the Tabernacle, and now the priests ministry on behalf of the people is laid out.
Leviticus is the guide to the cross. The gospels can, at first, appear light on explanation of the cross. Partly, they're narrative and narrative works by winks and nudges more often than by voiceovers, but the big exposition is found in books like Leviticus. Here we see what sacrifices and tabernacle (and temple) are all about. Here we see why a death is necessary, why blood is shed, how bad sin is, how great Jesus is.
The book reads like a list of laws, but it's the transciption of conversation - between the LORD and Moses - don't miss the action.
Jewish children would read Leviticus before anything else (Wenham's commentary). This is gospel basics.
Leviticus fits in the story of the Exodus and is well connected to the life of Israel as they do and don't practice the sacrificial system they've been given - it makes sense of much of Ezekiel and is widely quoted in the New Testament.
The big landmarks in Leviticus are the Day of Atonement in chapter 16 and the Jubilee celebrations in chapter 25, when the trumpets sound that atonement is achieved and jubilee rest is on. It's worth slowing down here to take things in.
Chapter 23 tells of the main feasts which retell the major movements in the salvation story of God's people which helps to interpret Jesus' attendance feasts and their place in the life of Israel... each of them remembering the grace of God and so singing of the gospel.
Broadly the book splits into two parts -- chapters 1-16 dealing mostly with rituals and 17-27 with ethics, but this isn't a divide to mark too strongly. The whole book is about holiness and what is pleasing to the LORD, and the whole book has to do with the coming of a final priest and sacrifice.
The best way into Leviticus I've found is this: (1.) Read it. (2.) Listen to these four sermons by Mike Reeves on Leviticus from a student leaders weekend. Yes, Leviticus is so gospelicious that we'd have it preached to 19 year old leaders to equip them for mission. (Free mp3 downloads after registering at uccf.org.uk)