The first thing you have to realize is that some people will ask you to prove God exists but not actually want you too. They don't want to accept the fact that they don't control everything and that their actions have consequences. So when encountering these people all you can do is pray that God will open their hearts and do a work in their lives.
One of the things to ask the person to see if they will actually listen to you is "What would you take to be acceptable proof?". Most athiests never thought this far ahead and it makes them see that they can't just throw away everything you say.
Step 1: Respect them
Most of the atheists you encounter will be smart and sincere. Don't belittle or talk down to them. They are way more likely to listen to you if you respect their intelligence.
Step 2: Find ways in which you are similar
Find areas in which you agree. Such as the value of science in todays world or that you respect the fact they want proof or evidence before they accept a belief. If you're talking to an athiest it is very unlikely that you have the same religious beliefs. So start off with what you have in common.
Step 3: Ask thought provoking questions
Ask them what they believe and why they believe it. Ask them what they think is the best argument for God and why they think it falls short. this will get them to think. It will also let you know where they're coming from.
This is also where you ask them what they would take as proof. Ask them "If God came down right here right now showed himself would you even believe Him? Or would you think you're hallucinating? If He the stars to write "I am God and I exist" would you believe Him? Or would you come up with a "natural" reason this happened?"
Because any responses you get for why God doesn't exist will be exactly like this. Hopefully this will make them see that they can make an excuse to everything but that doesn't make it true. Because God did in fact come to earth and proclaim I am God and there were still people who didn't believe Him.
Step 4: Present your evidence
Some different things you could point out is how Christianity is the most heavily persecuted religion. Other religions are persecuted but none are persecuted as much as Christianity especially in the United Sates.
Bring up how this is because the Holy Spirit does in fact convict people but people love their sin too much so they try to get rid of the one convicting them. Another point you can bring up is our moral compass. Why do we feel murder is wrong if we, like evolutionists say, are simply animals. We feel murder is wrong because God gave us a moral compass.
The next point would be to state why the universe exists. In evolution there's no point to it all. But everything that has ever been created has had a purpose. Pens are created to write, phones are created to communicate, and watches are created to tell time. Why would everything in the universe be created with a purpose except the universe?
There are so many more points you can use and we can't list them all in this one article. There are so many resources on different platforms such as Google and Youtube. Let us know if you have any further questions on the subject! Thank you for reading and we hoped this helped!