a) It works best, when doctors take their time to prescribe it, even if you know it's a placebo. There are studies about two groups where one receives a placebo and the other a placebo and a 10 minute talk. The latter had better outcomes.
b) The placebo effect works best, if used with symptoms of pain. This is the most-studied use-case for placebos. With a virus infection like a cold, not so much. See c)
c) Supplements like vitamin C generally speaking don't seem to really help when a cold is coming. As long as you have a healthy diet, supplements aren't required and don't really have a positive effect on your health. Maybe some stuff makes you feel slightly better, but it doesn't make the infection go away.
d) Not every cold breaks out. Sleeping helps a lot.
No consistent effect of vitamin C was seen on the duration or severity of colds in the therapeutic trials.