Our word "evangelism" entered into the language in the early 17th century, coming ultimately from the Latin evangelium (Gk. evangelion), meaning "gospel." "Gospel" itself comes from Old English godspel, from god "good" + spell "story, message;" i.e., "good news."
If evangelism is sharing this Gospel with others, how, then, are we to go about it? Blessed Cardinal Newman distinguished two types of conversion: intellectual conversion and "real" conversion. Intellectual conversion is the simple fact of accepting Christianity as true according to the dictates of logic and reason. This is necessary and related to "real" conversion, but it is not its essence. Real conversion is imaginal, meaning, to be really converted to Christ does not primarily mean accepting the theology. It involves this, but primarily it means the submission of one's very self to Christ, body and soul, so that one lives and breathes the Truth, quite literally seeing it in the world around oneself all the time.
This is exactly what the Catholic Church professes to do. By means of the operation of the Saints, the Sacraments, the Church itself, and the Holy Spirit the Church brings Christ himself to us continually. Our Lord even uses the Church to come to us in his very flesh. It is this Personhood of Christ, transmitted through the Church that we are called to bring to the world. This is why after Communion Mass wraps up fairly quickly. The Church is encouraging us to take what we've received, to take Christ himself: body, blood, soul, and divinity, out into the world without delay or hesitation. And this means a life lived in love (caritas), and loving sacrifice, even unto death.
Our first, most fundamental, and most important task when it comes to sharing the Gospel is living Christ in this way, so that we become conduits of not only the intellectual principles of Christianity, but the Truth himself. We must unite ourselves to him and his life so completely that others see him through us, as we live a life of love, service, and sacrifice.
To be sure, we must "always be prepared to make a defense to any one who calls [us] to account for the hope that is in [us]," (1 Pet. 3:15). But it is the Person of Christ which we are to transmit primarily. In other words, we are not called to argue people into the Church, but to love them into it. After all, that's how he goes about it.