How does one effectively overcome mental/emotional addictions, (Not physiological)?

By letting go of them.

Counseling.

Storm,
Both Harlan and joel are correct.

One thing to consider is the purpose of the addictive process. No behavior continues if it doesn't serve a purpose. The purpose of addictions both to external chemicals and behaviors (commonly reffered to as Compulsions) is to distract us from unpleasant thoughts, feelings and emotional states. The process of counseling helps a person to gently come to understand and face the things that they don't want to or cannot see for themselves. Every person on the planet uses different behaviors when they are in pain. When we use those behaviors repeatedly they become habit. The primary aspect as Harlan said is letting go of behaviors that at one time served a purpose for our "survival" that have now become problematic. The healtier a person is the more clearly they can see reality in all of it's fullness and bear the unpleasant aspects as well as the beauty...which can also seem unbearable. As both nature and nurture play a role in the equation we need to be both gracious and firm with ourselves and others as we address areas of personal struggle and growth.

What if it's a thing of pleasure or something?

Anything that is pleasurable or relieves pain, be it a substance, thought, behavior or person can be used by an individual addictively.With chemicals it is called substance abuse. With thought it is called compulsions and with people it can be called codependence. The challenge of living is to experience pleasure when it is appropriate and pain when it is appropriate. Managing both of those can be called temperance or moderation.

Mental addictions must be overcome as they are, mentally.

It's a matter of inner strength. The addiction has formed because you have conditioned your mind to feel particularly attracted to a certain thing. To break the addiction, you must break the mental conditioning.

How was your mind conditioned in the first place? Repetition. How do you break the conditioning? Repetition.

I'm not quite sure what you're addiction is, but the secret to breaking it is to simply repeatedly not do it. Every time you want it, don't have it. It'll be difficult at first, but eventually it'll be very easy to push the idea aside.

I quit both soda and burger joints this way.

Just realize that you can do it. It is not a matter of can or cannot... it is a matter of do or do not. Quitting is not beyond you.