When you approach a stranger to give him a booklet you don't know if he's religious, an agnostic, or an atheist. When you offer a booklet at the start, at least the person knows you are giving him something and he should appreciate that. At the same time you should have an introductory remark which catches interest. It could be in the form of an interesting question and not sound like you are challenging him. After all, you have his welfare at heart. We are to "love your neighbor as yourself" (Mt 19:19). Therefore be friendly and not argumentative. We were once in his shoes regarding being unsaved and we should have a humble attitude and not feel superior. The conversation should be informal but focused. You have an agenda to follow but should be receptive to questions that come up. Its possible to get off track, and time will expire without coming to a conclusion. An answer should be presented for the original question. Agreement would be a sign you are getting somewhere. If the person wants to think it over some more just make sure he's aware of the main points in the booklet as a reminder. Don't rule out that you can lead a person to Christ. Then thank the person for spending time with you. It would be beneficial to provide a phone number or e-mail address for asking questions
Various tracts are available for witnessing. World Missionary Press scripture booklets are portions of the Bible and each is designed for a particular purpose. You must thoroughly understand the message so you can explain it even if you're not referring to the booklet. Each point in the topic should have a reference to a place in the booklet. You should be so familiar with the booklet that you know immediately which page to refer to. A pregnant pause can cause the train of thought to be lost. By being conversant you communicate confidence and the person stays connected. Concentration precipitates thought which leads to comprehension.