I introduce them to Christ the Healer.
The salvation language is foreign to lots of people, especially when they don’t perceive themselves as sinners.
But almost everyone knows where they hurt, what needs healing. I may respond something like this:
“You know, one of the things that helped me even think about salvation was when I realized that Jesus brought healing to everyone who asked. Physical healing, emotional healing, spiritual healing. People who were powerful in their own way, and people who were the despised and ignored. I really came to believe that Jesus is who he said he is when I reached out for healing. [Insert personal story of emotional healing, because most people need emotional healing of some sort.] It was amazing, really. I was able to forgive that person, when before I couldn’t. Maybe that feels more relevant to your life right now rather than talking about salvation? I mean, who hasn’t been hurt?”

Depending on where the conversation went, I would share that people who receive healing from Jesus are in a safer, healed place and can become aware of their own failings–but they can ask Jesus himself to heal that breach as well. But if the person realizes that they could be in need of emotional healing (or any other type), I’d ask if we could pray for Jesus to enter into that need right now. Then–especially if they feel they have been immediately healed–ask them to go to Church and thank God for that healing. Ideally give him/her someone sympathetic to connect with, a local priest, etc. (Moving to sin and salvation would ideally be a second conversation.)

Hope that helps!