I wouldn't call it the defining mark of a Christian, but rather the mandate to the body of Christians.
It is possible that the statement is derived from
Matthew 24:14 And this gospel of the kingdom shall be preached in all the world for a witness unto all nations; and then shall the end come.
There isn't any mandatory preaching "methods" as preaching could be even defined as just giving testimony of what God has done in one's life and then offering the gift of salvation to be part of a new Kingdom life and living.
So something as simple as "Both my wife and I came from a divorced home and after 8 years of marriage we were heading in the same direction. After we both gave our lives to Jesus Christ, in 24 hours our marriage was filled with God's love and completely turned our marriage around.
That is the power that the resurrection of Jesus Christ can do in your life! Would you like to have your sins forgiven and have the power of resurrection come into your life? He loves you just as much as He loves me because He died on the cross for everyone" would be classified as "preaching to the world".
and again, as my friend does in India and Pakistan to tens of thousands of Muslims and Hindus,
"For God so loved the world, love you, that He gave His only begotten son so that if you believe on Him you will have everlasting life! And to prove it, if He doesn't do a miracle today, call me a false prophet and run me out of here"... and miracles happen and people give their lives to Jesus... that also would be classified as preaching the Gospel.
So it can take many forms and fashions... from one on one just answering questions or "preaching" the resurrection to the masses... Jesus just wants us to reach out to the world.
Does that help you?