How can I be a better witness?

The most important principle is to first be walking with the Lord in love and holiness and character (Galatians 5:13-26) and be growing in your relationship with Him – abiding in Christ, who is the true vine – John 15:1-16.  A holy and godly character gives you credibility when you open your mouth and witness that Jesus Christ is Lord and He is the one who has changed your life.  But witnessing is not only in good behavior, you have to open your mouth and testify that it is the Lord who has changed you and give glory to Him.  If you never open your mouth, then people will think you are good because of yourself and your own morality and that is not giving glory to God.  Rather that is giving glory to self.  

See this article here on learning to Share your Faith.