Many believers speculate what it means to, "work out your salvation" when it is clear that we are saved by grace and not works. But, James says, faith without works is dead.
In the same way, faith by itself, if it is not accompanied by action, is dead. - James 2:17
The "work out your salvation" passage is found in Philippians 2:12. Verse 13 gives us more insight as to what verse 12 means. God does the work in us and our job is to come into agreement with God. Agreeing with God means we take action. We become co-laborers with God. So, we are doing something, but it's God who is accomplishing it through our action.
Therefore, my dear friends, as you have always obeyed—not only in my presence, but now much more in my absence—continue to work out your salvation with fear and trembling, for it is God who works in you to will and to act in order to fulfill his good purpose. - Philippians 2:12-13