Cling to your faith in Christ, and keep your conscience clear. For some people have deliberately violated their consciences; as a result, their faith has been shipwrecked. 1 Timothy 1:19

How do you keep a clear conscience?
"Cling" to your faith in Christ MORE THAN anything else and do what you KNOW is right.
Let's face it, when we do wrong, we KNOW it's wrong, and we do it anyway. We're ignoring God, and each time, our hearts harden, until eventually our ability to tell right from wrong diminishes.
A Christ-centered life, a life where we listen intently when He speaks, makes right and wrong and everything in between, crystal clear.
It's not enough to listen to Him. When I was a kid, I "listened" to my Mom all of the time. Whether I acted on what I was told is a completely different story (sorry mom) :-). Don't just listen---ACT, and doing what is right/keeping a clear conscience won't be so much work.
Hold (cling) tight!
Peace!