Witnessing is a form of dying to ourselves to the instinct of pleasing of men--including ourselves--which goes to the root of the word witnessing in Greek: martus, from which we get martyr.
2 Cor 4:10-11 (Phi) Every day we experience something of the death of Jesus, so that we may also show the power of the life of Jesus on this bodies of ours. Yes, we who are living are always being exposed to death for Jesus' sake, so that the life of Jesus may be plainly seen in our mortal lives.Remember that our "testimony" is not a "spiel", or prepackaged script, but the truth about who we are and who God is, what we have done and what He has done. To this we must witness, and "reckon ourselves dead" to all else.
God hates trumpery and phoniness and has made this quite clear, so we need not pretend we know all the answers or are in some other way "prepared" to start. We ARE his witnesses, and as we speak of our own depravity (as opposed to worldly boasting and self-promotion) and God's goodness we will find those chosen by God will deeply resonate to this message by the power of the Holy Spirit.
As Jesus said in John 3, "we speak what we KNOW..."
Notice how Paul always tells WHAT HAPPENED to him--how God saved HIM--when "witnessing". Thus, we have the same story told three times in the book of Acts about what happened on the road. The telling, and re-telling, of this made him look like rather a chump, but this was the point. Remember it was Paul who said "God's strength is made perfect in weakness". So Paul boasted of his history of stupidity and deliverance, shameful as it was. This kind of "witness" is the hope offered to others that they too can be healed and made holy before God.
This is true "Christian witnessing". All else I call "Mormon witnessing"--the logical spiel--the program, the mental strong-arming, the sales-pitch, etc.
We simply are honest about our doubts, our deliverance, our impatience (like David--who had "a heart after God"), our failures, what He has done for us, His goodness, and the like--without exaggeration or hype--and let the Holy Spirit do the rest.
Col 4:5 (NAS) Conduct yourselves with wisdom toward outsiders, making the most of the opportunity.