The use of the Old Testament in the New Testament is an intriguing as well as often complex study. However, the fruits of finding the connections are worth the effort. There are numerous ways in which the New Testament uses the OT, but the below list, from Sydney Greidanus*, is just a few ways in which you can specifically look for how the OT points to Christ in your own Bible reading and Bible study preparations. [This is just a short synopsis of the categories he gives. Keep in mind that these categories often overlap and aren't necessarily exhaustive of all the nuances between Old and New Testament.]
- Redemptive-Historical Progression: This is about the progress/continued unveiling of God's revelation of Himself throughout time and how that revelation of Himself culminates in the person of Christ. Greidanus states that this is fundamentally about "connecting the dots" of Scripture, ultimately connected to Christ.
- Promise-Fulfillment: This is when there is a direct promise of something that we find fulfilled in Christ.
- Typology: This way of finding Christ is about foreshadowing-- through specific people, events, institutions, and places in Biblical history. The "antitype" to these things is Christ.
- Analogy: This is when there are parallels found between something in the OT and with Christ's personhood and/or teaching.
- Longitudinal Themes: Taking a specific theme in Scripture and tracing it from OT to NT, seeing how it culminates in Jesus.
- New Testament References: Looking for direct quotations and allusions to OT texts make by NT writers.
- Contrast: Many of the things in the OT act as "foils" - something that contrasts with Jesus to emphasizes how He is better and different.
*Sydney Greidanus, Preaching Christ from Ecclesiastes, pgs 25-29.