To "work out" one's salvation means to work in a way that is appropriate to one's salvation or to work in a way that shows one's salvation. The abstract noun "salvation" can be expressed with a phrase about God saving people. Alternate translation: "work in a way that is appropriate because you have been saved" or "work hard to do the good things that show that God has saved you" (See: [[rc://en/ta/man/jit/figs-abstractnouns]])
Paul uses the words "fear" and "trembling" together to show the attitude of reverence that people should have for God. Alternate translation: "salvation, trembling with fear" or "salvation with deep reverence" (See: [[rc://en/ta/man/jit/figs-doublet]])