One-on-one witnessing can be pretty intimidating.  There really is no "easy" way of breaking the ice to be able to share Jesus with someone.  No matter what you do, there will always be that split second where you’re just going to have to bite the bullet and just say something.  The more you do it, the better you will become and the easier it will be.  God will teach you AS you do it.  He’s big into on-the-job training.  (see Matthew 13:12) 
 
   The more we get over the worries of offending someone or being "effective" the more free we will become.  It’s quite comforting to find this verse:

1 Corinthians 1:18 For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God

    If you go into it knowing and understanding that you will appear foolish it really makes it easier.  It also helps you distinguish "those that are perishing".  As Americans, we need to stop trying to package the gospel in something more acceptable to the world.  Jesus never did.  The gospel message has been and will always be offensive to the world, ALWAYS.  It doesn’t mean we need to be weird, foolish, or crazy on purpose, it just means we need to be real about it.  What we have is better than what the world has, and we need to act like it is. 
 
    How would you feel if you had $1,000,000 to give to anybody you wanted (knowing that you have an unmeasurable amount of income in the bank and it isn’t an issue at all to give a million away)?  You would probably be excited to have the opportunity to give it to someone.  You find the first poor, beaten down person you run across and approach them thinking that they will jump for joy at the thought of all their worries fading away now that they have this money.  However, as you approach the filthy, hungry, poor person they begin to curse you.  Not knowing you have the answer to all their problems in your pocket.  You don’t let that bother you because you know once they see the gift you have for them they will jump for joy and dance at their new turn of luck.  You’ve put up with the curses and insults and you’re inches away from the person.  Now is the time!! Here it comes, the moment both of you were waiting for, only he didn’t know it yet.  You pull out your money and hand it to him.  Instead of him jumping and dancing, he curses more!  He hits your hand away and becomes increasingly violent pushing you and your gift away because of pride.
 
    What a surprise!  Imagine someone turning down the greatest gift the world has to offer.  Now, how would you feel about your gift?  You wouldn’t throw it away, or hide it, and never try to give it to someone else.  Instead, you would have compassion and pity for that person who couldn’t recognize what the gift would do for them.  Actually, if someone turned down our million dollars it would almost have an opposite affect to the point where we would say "This guy’s an idiot!".  We would never take on the feelings of being ashamed or embarrassed.  Instead we would be ashamed or embarrassed for the person who doesn’t receive it.  You wouldn’t be discouraged or embarrassed because it has nothing to do with you.  You’re just offering a gift.
 
    It’s no different than the greatest gift the universe has to offer…the gift of the Kingdom of God and restoration to the Father in heaven.
 
    Just as you wouldn’t hide your million dollars and never attempt to give it out again you can’t hide your testimony and the message of the Kingdom if someone refuses it.  It’s just as foolish, even moreso.
 
    That’s easy to understand and comprehend, but I don’t think that’s the real problem.  I think the root of the problem is that most of us don’t believe that what we have is better than what the world has to offer.  We want to believe it is, but our actions prove otherwise.  Until we believe everything Jesus told us, we will feel like we’re offering the world monopoly money expecting them to believe it will make their lives better.  What we have is real, and we have to believe that first before we can ever expect the world to believe it.