Therefore, my beloved, as you have always obeyed, so now, not only as in my presence but much more in my absence, work out your own salvation with fear and trembling, for it is God who works in you, both to will and to work for his good pleasure. (Philippians 2:12-13)
The doctrine of salvation by faith only minimizes obedience as having an impact on one's salvation. Yet, without an obedient faith one does not have a mature faith. Jesus warned it is useless to say "Lord, Lord" while not doing what he says (Luke 6:46).
In this passage the apostle Paul unquestionably links obedience and salvation. Christians are exhorted to bring their salvation to a full or complete accomplishment or conclusion. Reverent obedience is how God "works in you" to fulfill his will in your life.
"Work out your own salvation" does not mean everyone has to just find their own way to heaven. Nor does it mean you somehow earn your salvation. It means to develop a mature faith that genuinely obeys Christ with God-fearing devotion.