God will work through us. “The laborers are few.”
I did a lot of street evangelism all through the 80s, at the Ann Arbor Art Fair. I was an evangelical Protestant then, but I did go once or twice as a Catholic in the early 90s. It was always a great time and opportunity for discussion about theology and God.
(1) Short, catchy, colorful, “not too heavy” literature is definitely best for initial contact. The visual aspect is very important to make someone stop and have curiosity. I would highly recommend the tracts published by St. Paul Street Evangelization. I edited most of them. These are short and catchy and can help to start conversations. Or you could design one of your own if you have someone who can draw, etc. Anything that will get people to stop and talk is good.
(2) The first thing I always stress is that everyone is different. We must always try to see where they are coming from first, and then hone in on that place and go from there. This is what St. Paul did on Mars Hill in Athens: he acknowledged the truth he saw in the pagans there, commended them for it, and then built upon it in order to introduce the true God and the resurrection. Paul said “I have become all things to all men.” I've always tried to follow that approach in my apologetics. And always, we have to be charitable and pleasant about it.
(3) People appreciate if you listen to them and their concerns. It's human nature. We're all like that. They would rather be listened to than preached at. If you gently ask “probing” questions in a low-key, non-pushy, non-threatening way, a certain number of people will talk and even open up. It'll always be a small minority of the whole, but you will find some.
(4) If you don't know something, don't try to pretend that you do. People admire it if we don't have an answer to everything, because they know that nobody does, and they resent “know-it-all” types. That's the negative stereotype of Christians and especially those who evangelize. We have to defeat and overcome that image. You can always say, “I don't know, but I can study that if you like, and get back to you, or direct you to Internet pages where an answer is given.”
(5) I also try to avoid all “canned” presentations and like to be informal and spontaneous. This ties in to meeting people where they are at. No one presentation works for everyone. I never liked the “four spiritual laws” thing even when I was a Protestant. It was too canned, too contrived, too formulaic (even though it had a lot of truth in it and was not a bad thing at all).
(6) Always stress the Bible with Protestants, and don't quote Catholic sources because it will mean little to them. Find something that is held in common (love of the Bible, trinitarianism, etc.), to show them that you are “a real Christian,” and then you can slowly get into Protestant-Catholic differences.
(7) With Catholics, often they will have some beef with the Church or big misunderstanding, and that is where you start in the conversation: address their biggest concerns. If they are nominal Catholics who know little, try to sense if you can what will spark their interest and go there.
(8) With those who know nothing at all about theology, keep it basic (the gospel of salvation) and don't get into “Catholic stuff” yet because that has to come later.
(9) Start slow with “heavy” theology and let the other person determine where the conversation will go and deal with their concerns.
(10) Don't let (certain sorts of) people take you down a hundred different rabbit trails. Insist on covering one topic at a time before jumping into another. This is extremely important. Oftentimes, people use that technique when they want to merely quarrel and wrangle rather than seek truth and hear the whole reasoning for something. Atheists are notorious in doing this. Get them on one subject and do your best.
(11) Pray before you go, pray for each other, and pray while you are there: that God will give you the right words to say at the right time, and in the right manner, for any given person. This can't be emphasized enough. You might want to fast and do some form of penance, too, the day before.
(12) Have Internet sites and/or books that you can recommend to people who want to pursue it, and have contact info. for yourself (phone numbers or e-mails or Facebook pages, etc.) that you can hand out. Business cards work well for this purpose. That's supremely important, too, as a follow-up.
(13) Know that ultimately it is the Holy Spirit Who will melt cold hearts and cause someone to positively respond. It is never ever merely because of apologetics. It's a supernatural work of grace. Our job is to simply be there as God's vessel: to “remove the roadblocks.” But only God can move a person's heart. It's like the old saying, “you can lead a horse to water but you can't force it to drink.” In a way that is very good for us because we don't have to shoulder that burden and worry about it. We just share in the best way we can and let God move in hearts that He has already opened: ones where “the harvest is ripe.”
(14) Again, I want to stress to the utmost that the message and method have to be specific to the person. (see #2 and #5 above). It can't be “canned” (like a lecture). We have to meet people where they are at. Once we start talking we must approach it according to the perceived needs and wants of this one person. They'll appreciate that, and it will foster deeper and more meaningful, constructive discussion.
God will work through us. “The laborers are few.”