What is the most effectivtive treatment for  psychological codependency?

Probably counseling. That can be tailored to the type of codependency one is dealing with. That could mean aa or alanon, na, perhaps gamblers anonymous, maybe eating disorders programs. Depending on the seriousness of the codependency psychiatric consultation or medication might be needed. A very broad range of interventions potentially are involved in the process.
Probably counseling. What kind of problem does the person have you are codependent on? If it's drugs or alcohol it's called enabling & if it's massive obesity that is being fostered by the codependent person it may even be classified as abuse. The list is long with gambling, and even at times very pathologically joining in anothers delusional system in all cases diagnosing and getting treatment for both is necessary.
Psychotherapy. This is a process that will take some time & going through the experience can be as important as the information you gain from it. Look for a therapist that has experience with co-dependency issues.