Don't do it one on one. People hate that.
Get a big microphone and fire off a sermon into a crowd. People will listen if they want to. And even if they don't want to, they will listen.
I may be repeating someone else, but I sort of disagree with this statement. I believe that we can witness to people one on one, if we use the right approach. And that approach is
humility.
No one appreciates someone getting "up in their face" and being aggressive. However, a gentler approach, where you are obviously respecting the other person's space and right to privacy, may elicit a more positive response. Remember, we witness as much with our actions as with our words.
If you have access, many evangelical churches and organizations supply tools to use in "cold calling" (that's what it is); printed material of one kind or another designed to pique the person's interest in salvation. You can
respectfully tell people what it feels like to be confident of your salvation, and invite them to read the literature if they think they might like to be confident too.
The literature (which should be short and to the point) should contain a telephone number where you can be reached, and a sincere offer to discuss any questions they may have with them. It would be advisable, too, to have a backup "expert" that you can call on if the questions get too difficult, but in most cases Scripture is sufficient.
In most cases, the response to this kind of approach will be one of five things; (1) people will politely refuse the literature, (2) people will take the literature and throw it away first chance they get, (3) people will take it, read it, and do nothing more, (4) people will take it and call you back, and (5) a person will ask you to talk to them right then (Praise God!).
In the case of items (1) through (3), you have to remember that
it is your job to deliver the message. It is God's job to follow through on the conversion process. In the cases of items (4) and (5), even if you reach a fraction of the people you approach, the Kingdom of God is enriched through your efforts. In the meantime, you are sowing many seeds which may lead to a wonderful harvest somewhere down the road.
In case somebody should get the wrong idea, I must confess that I, myself, am painfully shy and would have a great deal of difficulty in following my own advice.