The most important book you will read for the rest of your life will be God's word, the Bible. Making daily Bible reading apart of your life is an important first step in growing in the Lord. There are also lots of other good Christian books that will help you mature, here are some favorites for new Christians:
The simplest answer is because Jesus tells us to. Jesus said in Matthew 28:18-20: (NIV)
“All authority in heaven and on earth has been given to me. Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.”
To illustrate the point, imagine that you were a scientist and you had discovered the cure for cancer. There are millions of people in the world dying of cancer, what do you do? Simple, you give people the cure you discovered so they can live. It's the same thing with sharing the gospel; people are dying everyday without knowing the Lord. These people will spend eternity separated from God in hell. But we as Christians have the “cure”; we know who can save these people from hell- Jesus- we need to point people to Jesus so they can truly live.
The best resource to help you with sharing your faith in a way that will lead to true repentance is the site www.wayofthemaster.com check it out!
This can be one of the most difficult things when you become a new Christian. As your friends and family see changes in you and hear you talk about your faith the reaction isn't always pleasant. Your friends and family are going to expect you to be the same person you've always been but when the Lord saves you, you become a new creation in Christ and are instructed to flee from sin. The friend you used to go out drinking with isn't likely to be thrilled when they find out you aren't doing that anymore. They may be angry with you or make fun of you. You may lose friends in the process. It isn't easy but stand strong in your faith for Christ and pray that God will change the hearts of your friends and family. Also surround yourself with other Christians who can pray for you and encourage you.
God speaks to us through his word and prayer. Nothing that the Lord will want you to do will ever go against His word. When you're faced with a decision in life God's word is the place to go. Also have other mature Christians pray for you and offer their wisdom and biblical advice to your situation.
It means that your walk with Christ penetrates all aspects of your life. Your family, finances, workplace, school, relationships, thought life, everything. God wants all of you not just the “you” that goes to church on Sundays. No matter how long we've been Christians it's important to pray that the Lord will rule in all areas of our life. In the Billy Graham Christian workers handbook it says to encourage a new believer in the five basic activities of Christian life which are:
Going to church, praying, reading His word in the Bible, praising Him through music, seeing Him in all areas of your life and giving the credit to Him.