I would say the foremost thing is to maintain strong bodhicitta. That helps us not act from a place of ego or pride when talking to people about the path.
Its best to refer to books, authors, texts and teachers. If you can place a book in their hands without any attachment to getting it back (even if you say you are just loaning it) thats best. In fact you should tell them that they can borrow it even if you intend to never get it back because people often reject gifts, and you don't want them to reject the gift of a Dharma book. It creates a physical condition and cause in their reality to embark on the path or at least express further interest in it. Even if they don't read it for two years, it creates an opening for them. A conversation on the other hand can easily be forgotten 15 minutes from now.
In general its hard to know how to help others when we are full of delusion. Even if we are not *full* of delusion, even a single delusion or poison can propagate at the wrong time and cause us to act with ego rather than selflessness. At the same time we should not be afraid to share Dharma. After all its their karma that they come to us as opposed to some realized master. All we can do is to do our best to be of benefit to them and hope that they find their way.
That is a really good point, about how giving them a book is a condition that creates an opening...I've "lent" people dharma books in the past (without expecting to get them back) but never really thought about it like this before.
For a North American with no background in Buddhism or meditation, I would recommend The Experience of Insight
by Joseph Goldstein. It's basically a series of dharma talks and Q & A sessions from a Vipassana retreat. It lays out the basics of the Buddhist path, contains some basic meditation instructions, and answers a lot of common questions (i.e. "if there's no self what gets reborn?" etc). Goldstein is part of the Theravadin Insight Mediation tradition but he draws on a lot of different sources in this book, including masters of the Tibetan and Zen traditions. I think it is an excellent book for beginners, it is thorough and easy to understand.