Know one knows the kinds of steps--the bumpy ones, the ones that almost fell through, the ones that had gum stuck to it, maybe puddles in it--that one has walked in during their life. We don't know their trials and tribulations until we get to know them, that takes time. But if you are not genuine when you do this, it will show. And the person will close up, time's up. Ask the person if you can pray for them and what they would like prayer for. Most people will not turn down someone offering to pray for them.
If you are have a difficult time emotionally in wanting to go talk to someone you know has bi-polar, for example, but you feel you have no idea how to relate to something like that. If you are genuine, that person will appreciate you taking the time to get to know them. But they might not be used to it and it may feel strange. It may be awkward for them. So, if they act in a way you didn't expect, don't give up. Try again some other time. It may been a bad day for them. Don't let it drop there. Ask a brother or sister in Christ to sit next to you during the service. That will make them feel included. I would suggest same gender to same gender.
It's easy to do nothing and turn away, pretend they are not there. But that doesn't help them OR you. Think about why God designed fellowship for believers. No one is exempt if they take medicine of any kind, or have a disease or illness. How do you think prayer requests get passed around to other believers unless they know someone who is in need of healing from God. Help someone get connected to others and connected to Bible studies and any other groups that would be beneficial. They need that fellowship connection too.