My suggestion is to be Christ, to live an authentical Christian life of prayer, service, pennance and peace.
When you love others, forgive those who insult you, help people whom will never give you anything in return, deny yourself, work hard, frequent the sacraments and are at great peace, people will notice. When the world is in a rage and everyone is freaking out, and you go about your day calmly, not distracted by the crisis of the day but stay focused on what is in front of you, people will want to be like you and ask you how to do it. That is the time to start talking.
I have come to the conclusion that 99.999% of the time, talking about doctrine and dogma are a waste of time and breath. People don't want to know about doctrine and dogma. They want to know why their life stinks, why their husband had to leave, why the dog had to die, why their son is on drugs and why they never seem to find this joy and peace that Christians are always talking about. People aren't interested in doctrine. People want healing, forgiveness and peace in their lives.
If you can demonstrate a life of joy and peace, then people will be attracted to you like moths to a flame. The worst thing we can do to anti-Catholics is preach the gospel and not live it. We have to be able to demonstrate Christian lives, and authentic Christian living starts with prayer, not with doctrine.