As a general comment, I’d say to stick to what you are comfortable with and go from there. Don’t engage people in a setting where you’re not wanted. For example, people don’t go to night clubs so they can hear about religion, so if you go to a night club to give dawah, don’t be surprised with the responses you get. Another thing is to be familiar with the religion. If you simply pray and fast because of habit without understanding the purpose behind these actions, it’s going to be hard convincing other people why doing these things are important. Often times with other religions, you’ll hear people talk about what they believe or what they think when talking about certain subjects rather than giving facts. In Islam, we base our belief and actions on the Quran and sunnah, so without a solid understanding of these, you will fall into saying things like “I believe we do this because...” which opens the door for errors and misinformation.
Another thing to bring up is dawah isn’t limited to simply standing on the street handing out flyers and engaging with strangers. Dawah can be done with family, friends, or even other Muslims who you see deviating from the religion. For someone starting out, it would be easier to talk with people who already have belief in Allah but are misguided, vs someone who wants nothing to do with religion at all. Sometimes, your actions can speak louder than words as well and people will take notice of that. Look at the examples of prisoners of war at the hands of Muslims and ended up converting based on their observations of them, or even those prison guards from Guantanamo who converted because of the actions of the prisoners.
One last thing is to not be too forward with people or even approach people who are not interested. Often times when I walk through the downtown area for my lunch break, people will run up to me trying to offer something for sale, tell me about a new song they came out with, etc. I’m on my way to lunch. I’m not there taking a stroll for fun and honestly don’t want to hear what you have to say. People who are out and are interested in wanting to hear what you have to say will approach you if you’re out there with flyers and what not. Those types of people are more willing to take the time to hear what you have to say vs those that you approach randomly.
All of this is just my opinion of course, so take from it what you will.