Contains digressions, perhaps.
Since the early days of Christianity, preaching was perceived as the best ways to convert people. It is still used widely, and equally widely, it has a nasty reputation. Jehovah's witnesses are the only religious folks who ever knocked on my door here, but Mormons are known to do the same in North America, and probably elsewhere as well, I just never had those at my own door.
For all I know, nobody likes a preacher at their door. When the witnesses knocked on my door, I opened, and they kindly explained who they were, and stated that these days it was hard to believe in God, which I acquiesced to, and expressed my personal lack of desire in talking with them in my living room, after which they departed without further insisting, leaving me with the impression that people talk worse of them than they are. I am not, however, condoning their beliefs or the way they function, but they seem courteous when they preach.
Now, why is preaching pointless according to me? When was the last time you changed your mind because someone else was of another mind than you? If the person produces arguments and reasons that prove to you that you are wrong, or could perhaps make do with some further insight, then sure, but when it comes to things of faith and God, it is more complicated and more subtle, and mostly, it is not something you can just tell people and have them be converted. At best, you can intrigue them, but that is best done by one's behaviour than by one's words, all the more when they are preaching words.
As soon as you are seen as preaching, you might as well shut up, because no one listens to a preacher any more. Nowadays, it tends to cheapen whatever you have to say because of your sounding like a commercial for a product. That said, having never been exposed to real extensive preaching from any religious person, they might be more effective than I know, and so perhaps preaching isn't as counter-productive as I think.
Now a word about people who hate "those religious idiots who try to impose their beliefs on us". I can't stand it whenever I hear that because it oozes with stupidity. Dear non-religious person, you have to understand this one single thing: the preacher usually believes in what he preaches, which means, he thinks it is true, not just for himself, but for you as well. You don't have to agree with it, you merely have to accept that for this person, it is the truth and not an opinion. A Christian preacher will typically believe that unless you have the Christian faith, you are going to burn in Hell for eternity. Thus, if he shows up at your door and means to talk to you, keep in mind that he is trying to save you from a dire future. What does the preacher have to gain from talking to you? An unpleasant and frustrating time?
You can't preach against people's will, and that's why preachers won't insist if they see you're not interested. So much for "imposing beliefs on others". Besides, you can't impose anything, so let's not be capricious princesses about being exposed to other systems of beliefs. If you don't believe in this or that, and firmly so, no matter how much anyone talks to you, it won't change your mind, will it, so they can't impose their beliefs on you, therefore stop being so insecure about your own opinions and take it like an empowered person.
If Mormons showed up at my door, I'd let them in, bombard them with questions and see how they are and what they answer to me, and what they preach to me. I would not be annoyed a bit, as I'm interested in everything. And just because these humans believe in different things than I, doesn't mean they're any less worthy of my respect, or me theirs. I'll take religious folks a billion times over a single interview with a salesman.
Better than preaching, in my humble but educated opinion, is action. You can of course act with words too. But it will be infinitely more convincing and inspiring to see a Christian living his life in a Christian way than have him tell you about Jesus. If I tell you Jesus kicked ass and God is Love, you can only take my word for it and giggle somewhat; but if, out of Love, I help you out of some nasty troubles, lend you money, take care of you, etc, then I'm proving that I don't just talk, but that I act too. And those acts will speak much more to you than whatever I could say. Sometimes I think the only reason why Christ died was to talk of Love in acts, and that people would listen to that more than if He had been just words. See, you can believe that Christ was wrong, but you cannot say that He didn't love you. Suppose He was indeed wrong, well, He still believed that He was going to be tortured for you and me, and that much remains true even if the entirety of Christianity was a lie.
As a matter of fact, if you read the Gospels, Christ spends most of His time doing things; sure, He also preaches, but never like a salesman. And remember that, in the words of John, Christ is the word made flesh, which has never ceased to fascinate everyone ever since that was put down in words. Christ spent his time walking from town to town, healing and curing people, talking to them about love. That's how He converted people, and that's how His disciples did too after He died (physically). Nowadays, we don't think of Christians as healers, yet, such people do exist, under various names, and I don't know that they put their beliefs forward much, but they exist. At any rate, every primitive Christian was a healer because of the Holy Spirit, and could heal and cure people as well as transmit that Spirit. The fact that a Catholic priest can't heal you is perhaps a reason to think that the Holy Spirit isn't that much with them as they think it is, but that's a mere guess.
The fact remains that if your daughter was sick, and a Christian came to your house, offering to heal her, and did so, you'd see Christianity in a wholly different light. You'd give Christians, at the very least, the benefit of doubt, and you'd be inclined to listen to what they have to say. Blessed are those who don't need to see, said Christ to Thomas, and indeed so, yet Thomas still got to be shown what he needed to see to believe. You cannot blame people for not believing you on your words; if they did, they would believe you, but they would believe anyone else too. If I came up to your house preaching about my God - the Great Pink Kangaroo - would you just take my word for it and be converted? Of course not, and so you can't expect people to trust you on your word. However, you can expect them to trust that you yourself really believe in what you believe, which, in my case, would be an argument.
God didn't give you a critical mind for no reason. Being critical helps you avoid Great Pink Kangaroos and the likes, while it leads you towards the Truth (and I'll state for the record that this Truth I speak of remains mostly unknown to me). So be critical, but unbiasedly. You cannot be critical towards Mormons, and not towards atheists. You have to make sense. And this goes for preachers and preachees alike. To non-religious folks, one last word: don't think your non-religiosity is anything else than a belief too. To know something for absolute certain, you'd have to be nothing less than God Himself; since you're just a human, your knowledge is limited and so are your means to determine what Truth is; thus, anything you believe is just that, a belief, whether it is that God exists or that He doesn't.