How much prune juice will help relive my constipation?

May or may not help. Prunes/juice can help, but it does not work for everyone. I have never seen or heard of prune-overdose, so enjoy as many as you wish. If not better in 2-3 days, try miralax, (polyethylene glycol) fibercon, senokot-s, colace, Metamucil etc... For quicker relief, enema may help. Occasional use of milk-of-magnesia or mag-citrate for really-backed-up cases. If persistent, consult doc. Good luck.