There are four approaches believers sometimes default to when approaching strangers to talk about God. You'll want to avoid these approaches like food from a trash can: 

#1 Hesitation. If you think too hard about it before doing it you'll talk yourself out of doing it. Faith does not trust one's own abilites but God's. The opposite of faith is self trust and this always leads to failure.

#2 Too Agressive. When boldness starts eclipsing compassion and politeness it becomes rudeness. Think about how you would want to be approached (or not approached!) and act accordingly. Give the person a chance to comfortably turn down your inquiry to ask questions about faith and God. 

#3 Overly sensitive. Yes, there is such a thing as being so sensitive that it makes the person uncomfortable and communicates that what you want to talk about is obviously not that important. Don't apologize for nothing and says things like, "You're probably really busy right now, and this is probably a really bad time..." You might as well as him to outright reject you. Be bold about what you want to talk about and ask him with all politeness, but not as if you're greatly inconveniencing him. 

#4 Rabbit trails. When your friend brings up objections that will drag you down an irrelevant rabbit trail, acknowledge his question, and tell him you will get back to that, but first you wanted to know...