Well im no master, but ill teach you what i know.
Ten Original Sheikh Haroon steps to give da'wah
1) Seek refuge from Satan, and ask Allah to help you.
2) Remember it is your job to convey the message. Allah converts hearts.
3) Never speak to them as if you are better than them.
4) Never speak to them as if you know more than them.
5) Never speak to them as if you are right or are "holy" and they arent.
6) Never twist the faith, nor water it down to prove a point.
7) Dont just throw quotes at them ~ what will they mean? Use wisdom.
8) Relate to the person, try to be empathetic.
9) Show them how your path is noble, and peaceful. Show them (via your character) how this path of yours has made you a better person. If you sit there proud and arrogant, then they will take it that being part of the religion makes you so, which is obvious a bad promotion for da'wah.
10) Be kind to them, care for them, and let them know that Islam has the answer to every single one of their problems.
The best way of giving da'wah is by yourself. The way you walk, talk, act, look, everything is da'wah. Dont get angry, dont shout. Stay calm and collected, and stay reasoned. Some people have a habit of being annoyingly persistent ~ this is a terrible put off when giving da'wah. Give it when the person looks like he is taking it in. Dont just keep talking. Dress with free clothes. Not necessarily anything special, but free, open, inviting. (Take my clothes as an example, i explain to the non-Muslim that i wear these because they symbolise freedom, as they are open and flowing, the symbolise justice as they are pure and white, and they symbolise liberation as they are not aggressive, nor boxed-in.) You have to use the right approach. Dont be arrogant, and dont be proud. Come across as someone who is trying to relay something close to their heart.
These are but a few pieces of advice that i can give you, and may you and me, and everyone benefit from them.
And Allah knows best.