The Old Testament is just as much God's Word as the New Testament, and God has many treasures in it for us if we'll only take the time to discover them. Remember: "All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness" (2 Timothy 3:16).
It's true that we no longer follow some parts of the Old Testament the way people in those days did. The reason is because they have been replaced by what Christ did for us (just as the Old Testament said He would). For example, we no longer practice animal sacrifices and the reason is because Jesus Christ became the final sacrifice for our sins when He died on the cross. The Bible says, "For Christ died for sins once for all, the righteous for the unrighteous, to bring you to God" (1 Peter 3:18).
But the Old Testament tells us many truths about God we need to know, and it also shows how He preserved His people so His salvation could come to all the world. It also gives us many examples of men and women who walked with God, and we can learn from their lives. The Bible says, "For everything that was written in the past was written to teach us" (Romans 15:4).
Let me suggest you begin with the book of Psalms (which has been called the "hymn book" of the Bible). Then expand your reading to Proverbs, which gives us practical wisdom for daily living. Then turn to the lives of some of God's people, like David or Job. When you do, the Old Testament will come alive.