As already mentioned yesterday, Catholic evangelism is more all-encompassing than is the protestant view of evangelism. The self-stated goal of most protestants in evangelism is merely to get someone to "believe" in Jesus (which often encompasses no more than a couple facts about Christ's work on the cross). The goal of the Catholic who is seeking to explain the gospel to a lost soul involves a bit more; quite a bit more. The Catholic is also trying to bring the person to love God with their heart, soul, mind and body. Yet, evangelism does not actually stop there. When the Second Person of the Trinity was incarnated in human flesh, it was not merely to do a "last ditch effort" to get a few souls up to Heaven. He came to restore what was lost at the beginning of creation when Adam and Eve fell.
When Catholics consider the fact that Jesus came to "save the world" they take this truth at face value. Evangelism is not a "salvage operation" nor is it a cry of "retreat" in hopes that someone might listen and get out before the end. Evangelism is God's chosen means of expanding the Kingdom of Christ in this world; and that does not mean just a little expansion. When a Catholic properly seeks to "evangelize" people, he is enlightening them about the massive event that is going on already: this world is being saved.
Jesus did not come to save just a bunch of souls (and forget about the rest). He came to save the "whole world". As it says in one passage of Scripture, it was God's plan all along to "unite all things in" Christ (Eph 1:10), and in another place we are told that God will "put all things in subjection under [Christ's] feet" (1 Cor 15:27). To imagine that God created this vast universe (and other universes if they exist) and is not going to redeem it misses the point of creation. Now, the "problem" (for want of a better word) to this spread of the Kingdom is that not everyone wants Christ to spread His Kingdom. There is nothing they can actually do to stop it, but they do their utmost to make sure that they are not a part of it. This is the point of the evangelistic message: "Christ is taking back the world, reshaping it in His own image, and He wants you to be a part of this" (cf. 1 Cor 15:24ff for this type of image).
Therefore, when a Catholic is seeking to do evangelism, he is telling others that they have the opportunity to be part of this expanding Kingdom, and they do that by joining the Catholic Church (which is Jesus' primary means of expanding His Kingdom). This is much larger than "get your soul saved" and is nothing at all like "just believe in Him and you can go to Heaven". Those ideas have a certain measure of truth in them, but as with most of protestantism, they are a truncated version of the truth; reduced to the point of being almost unrecognizable. There is no place in this creation that Jesus does not say "that is Mine and I want to redeem it", but there are many people in this creation who (at least until they hear the gospel) say "I don't want Jesus' redemption".
This is why the Catholic Church works to redeem things; like when it abolished the Saturnalia celebration and replaced it with the celebration of Advent and Christmas. This is not "baptized paganism" as many protestants claim. Rather, it is redemption. If we seek to convert people, why would we not seek to convert the world that people live in? Everything about this world is subject to the redemption of Christ, for He came to save it all. Years ago someone complained to me that I wanted to "take over" the town we lived in and make everyone convert to Catholic (they did not know the half of it! I expect Jesus to "take over" the whole world!). A protestant once defended his method of evangelism by saying "you don't polish brass on a sinking ship, you just get the people off". Although it is true that you don't polish brass on a sinking ship, you could get the people to fix the holes in the ship (and that is precisely what evangelism is about!).
This is one of the reasons why Catholic evangelism can be difficult. We are not just seeking to explain Jesus' conversion of the sinner, but of the entire world. There is no way properly to write a mini pamphlet that encompasses the full concept of Catholic evangelism. I have seen some that have been printed by various Catholic organizations, and the best of them will just "begin the conversation". They say, "here are the basic facts, if you accept this, then head over to the nearest Catholic Church and get the process going". That, in principle, is the right way to open the doors, but it is never enough in itself. Explaining the redemption of Christ to people today can never be just a few facts, because becoming Catholic involves more than just a few facts (or "spiritual laws" as some protestants like to say).
When you approach family or friends who do not know Christ, make sure that you are not just giving them "tidbits". Evangelism is not something that can be accomplished in merely a couple of minutes. Even the Apostle Paul in his evangelistic efforts that we read about in the book of Acts would always take aside those who responded to his message and "explain to them the gospel" (the truths of Christ). Let us make this our effort as well. Christ is doing a great work, and He gives us the opportunity to be a part of it. Let us join with Him, and call others to do the same.