About one third of the entire Bible is prophecy. And Scripture has more to say about these last days then any other period in history. Obviously prophecy is very important.
As you’re out and about it’s easy to use current events to start a discussion. For example, while getting your hair cut you can ask, “What do you think about this crazy weather?” or “Why do you think there is so much turmoil in the Middle East?” After they respond, you can explain that the Lord said “the seas and the waves” would roar in the last days. And the Apostle Paul explained that the whole creation would groan and labor with birth pangs as delivery drew near.
Concerning the Middle East, you can explain that the Bible foretold that, in the last days, Jerusalem would be “a cup of trembling” to all surrounding peoples. And that Israel would be the epicenter of Bible prophecy.
By knowing a handful of last days prophecies you can quickly swing the discussion to eternal matters. I’ve used this approach many times – sometimes with only a couple minutes to speak. Then I’ll leave them a Last Days Prophecies booklet explaining that the booklet references many prophecies that they can look up and concludes with why all this matters. Why don’t you pray and give it a try. It may be the seed that leads a soul to eternal life.