One thing you have to recognize (that I’ve learned coming from atheism to Catholicism) is that you won’t “win someone over” by trying to beat them over the head with facts and arguments. Your goal is to plant the seed and let the Holy Spirit or God water it. That’s not to say you can’t engage in these discussions, by all means you should because it will help you learn how to defend your faith. But conversion comes from within the person.
To answer your question, the most effective way to plant the seed will depend on the person and how strong their convictions are of atheism. Some peoples’ hearts are so hardened that it will be futile regardless of the arguments you provide. Others may be scientifically/philosophically inclined, in which case reason (Aquinas’ proofs are a good demonstration of this) may work (and, in fact, that’s what helped reel me in). Others may be swayed by emotional arguments, though if they’re an atheist, they’re more than likely going to want harder proof than a one-off miracle or “soft” argument.
Most importantly, I think you just need to live the faith when you’re around them. Don’t be constantly seeking “the right argument” to get them on “your side”. Be a good friend and someone they can trust. Share your views with the utmost charity and compassion. Putting them on the defensive every time they’re around you will immunize them to whatever progress you may have otherwise made.