I agree with Pbiwolski's post, there is some good advice there.
This may sound worldly, but for years I was an insurance salesman, and one thing I learned is you cannot really "sell" anything to a person who is not first
interested in your product.
Now that doesn't mean you should wait around for someone to express an interest in going to heaven. Sometimes you can create that interest. I remember hearing the preacher preach about how terrible hell was and how a person who goes there is lost forever without hope when I was an 11 year old boy. That absolutely got my attention, and I almost ran down the aisle at the invitation. I could not wait one second longer, I wanted to know how to be saved right then and there!
I don't think it is bad to ask someone if they would like to know from the Bible how to go to heaven. But look for genuine interest. Some folks act interested just to be polite, but when you start showing them verses you can easily tell they want out of the situation. So you have to pay careful attention to them, and if you sense resistance, that is the time to back off. Then you can hand them a good Bible tract on salvation, ask them to read it, and tell them you will be glad to help if they have questions.
Now be on your way. If you make a person angry they will put up a wall and never listen to you.
I also agree about asking questions to determine what a person already believes. This can tell you what verses to show them. A Roman Catholic for instance does not think a little white lie is enough to send them to hell. Then you might show them a verse(s) like this:
James 2:10 For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all. 11 For he that said, Do not commit adultery, said also, Do not kill. Now if thou commit no adultery, yet if thou kill, thou art become a transgressor of the law.
This is when they usually start getting angry.
But look for conviction and sincerity. If a person is genuinely convicted, they will listen to the truth.
I remember a young fellow I worked with years ago. He was very rough around the edges, cursed a lot, and was missing all his front teeth. I used to talk to him about the Lord, and even gave him a Bible tract. He was a little intimidating though. But one day he came up and started talking to me about Jesus. I told him that he needs to realize he was a sinner and ask Jesus to forgive his sins. He said, "I already did that the last time you talked to me". I was surprised and said, "You did?" He said, "What do you think I am, stupid? I'm not going to Hell. I asked Jesus to save me!"