εὐαγγελίζω euangelízō, yoo-ang-ghel-id'-zo; from (G2095) and (G32); to announce good news ("evangelize") especially the gospel:—declare, bring (declare, show) glad (good) tidings, preach (the gospel).
-a bringer of good tidings, an evangelistthe name given to the NT heralds of salvation -through Christ who are not apostles
Evangelize really does mean to bring good news. The angel's appearance in Luke is definitely speaking as an evangelist today of good news for all mankind:
And the angel said unto them, Fear not: for, behold, I bring you good (G2907) tidings of great joy, which shall be to all people. For unto you is born this day in the city of David a Saviour, which is Christ the Lord. (Luke 2:10-11 KJV)
The problem often is that people see an evangelist as a person who is full time dedicated to telling people about Christ. A good many of them are full time, but this is also a part-time work for full-time Christians.
There are so many was of sharing the gospel, that really good news, with a wide range of people. I've shared it simply by asking people to come to our church. I cannot think of a church sponsored event we've held that doesn't include at least a moment of prayer plus touching upon the good news that Jesus is interested in every one of us.
For me, the really good news is that Jesus was born, lived as any person, taught His doctrine for three years, defined Himself as God, died in a single event, was buried, and on the third day was resurrected, appearing for forty days to those who knew and loved Him. That story was part of the prophesies that Judaism had carried through centuries, and that Christ's followers (first called Christians in Antioch) preached the first century.
Two of the best examples came from Paul. I've written about his testimony before Agrippa recently, and a couple of times in the past years - that is most definitely telling a specific person what Jesus meant to Paul's life. A huge change from a Pharisee condemning Christians to an evangelist speaking of that change to a man who literally held the life/death decision for Paul. The second example is in Athens, where Paul spoke so close to where Socrates was condemned to death. There Paul shared the gospel with people who spent a lot of time thinking about a wide variety of subjects.
Some of his hearers at Athens mocked Paul, while Agrippa closed their meeting as almost persuaded. Others in Athens wanted to hear more, and some believed.
"Believing is a matter of the will. A man does not believe without being willing to believe."
C. H. Spurgeon 1834-1892
We have control over whether we believe what the Bible says, or not believe even a portion of it. There is no denying the words in the Bible have been preserved for thousands of years, even though written on destructible papyrus by men who passed it down from generation to generation. Those who truly believed we should follow this:
Hear, O Israel: The LORD our God is one LORD: And thou shalt love the LORD thy God with all thine heart, and with all thy soul, and with all thy might. And these words, which I command thee this day, shall be in thine heart: And thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up. (Deuteronomy 6:4-7 KJV)