Well first off, praise The Lord that you even care about witnessing to people. A lot of Christians don't and are content being on the sidelines. But here are some tips:
1. Pray -- Pray for confidence, pray for the right words, pray for good timing and the hearts of the people you interact with. We do all things by Christ who strengthens us.
2. Start small -- Get tracts of DVDs and just start leaving them places. Leave them in stores, on the train, at the ATM. This is a very conflict free but effective way of spreading the Gospel.
3. Invite people to your church -- As someone who witnesses on the street A LOT, I find one of the easiest ways to witness, it to just say, "Hi, I'm from People's Baptist Church on 27th street and we are inviting people to come out and I wanted to invite you" and from there start discussing the Gospel or asking about their beliefs. People really like to be invited to things. Even when they have no intention of going. You'd be surprised. This again is where tracts come in handy because when you are closing your convo, you can say "we're also giving out Gospel literature." and give it to them. I think it's one of the easiest ways to get a person ready to talk and at a minimum take the Gospel from you. All the best. Just remember, we only plant seeds, God provides the growth. God bless.