Jesus likened evangelism to fishing.
When you want to go fishing, you need to have some bait that will attract the fish to you before you catch it in your net or hook.
This is the same way we must approach evangelism.
Paul wanted to win a community for God. Having noticed that they we already ignorantly worshipping god at an altar dedicated to "The Unknow God", he decided to start from there.
If you make it obvious while approaching people that you have come to preach the gospel, they are likely to put up a front, but if you approach them with a possible point of interest and they warm up to you, then you can present the gospel to them.
When you want to preach to someone, find out their interest or curiosities first, then start form there. If you approach a person to discuss his/her area of interest, you would definitely get their attention and then you can present the gospel afterwards.
One day, I was on a plane and seated beside me was a man who had on gold necklaces, a gold wristwatch and even his walking stick was gold.
if you are talking to politicians, tell them Someone somewhere has been a leader even before we were all born and no one has ever been able to overthrown Him. If you are preaching to a farmer, speak the language of farming that he understands.
Get good knowledge about the person you are to preach to and approach them from their area of interest.
The Holy Spirit will do the rest.