I see a lot of misunderstanding in the article and in the comments here that I would like to address. I am very familiar with NA, AA's narcotics-focused sibling, having found sobriety for 15 years now. I will be saying NA, but please understand that what I say also applies to AA.
I never really understood why the twelve steps work, until I did. This is a long and rambling explanation of what I have learned.
If an actual cure for addiction was found, almost everyone in recovery would jump at the chance. The view in NA is that addiction is a disease and that there is no cure the best we can hope for is being "in recovery" as opposed to being "in active addiction".
There are three main phases to a success story in NA: the newcomer, the sponsor and the relapse. All three are necessary for long-term treatment of addiction.
The newcomer is a very emotional person often burying their emotions at the expense of those around them. Imagine the cognitive dissonance of one who loves their family members, but steals from them all-the-same. There is nobody with whom to discuss these feelings outside of NA, nobody who will understand. This leads to coping strategies which are unique but ultimately ineffectual.
Addicts typically exhibit above-average intelligence. It is very difficult to maintain a $200 per day addiction while your social skills, dependability and general appearance are quickly declining. This intelligence allows an addict to continue in life by "working around" the issues they encounter until that becomes impossible, this is what is referred to as "rock-bottom". At rock bottom the only choices are jails, institutions, death or recovery. For those lucky enough to seek recovery, NA provides a vocabulary and tool-set for correcting those the issues which have been piling up in the addicts life.
The twelve steps start off with three steps which are impossible to achieve without hitting rock-bottom. Admitting powerlessness over addiction, believing that there is a power greater than oneself which could restore sanity and making a decision to turn one's will and life over to that higher power. Once an addict is ready, these steps take very little time to complete.
The remainder of the steps walk one through the process of coming to terms with their lies, justifications, crimes and other misdeeds. Often the last 9 steps are just repeating your inner-dialog of the past few years out loud with another person, because it is hard to hide the faulty logic when there is someone actively listening.
Once an addict is able to face reality, it is important to engage the community and to start collecting responsibilities such as making the coffee before the meeting or setting up the chairs. These small responsibilities provide a way to prove oneself to the group as well as to oneself. The responsibilities allow an addict to begin rebuilding a life where they are used to being relied upon.
Once someone is able to feel good about where they are in life, it is time to move onto the next phase, sponsorship. It is easy to justify relapse once you are in a good place, after you managed to crawl out from rock-bottom. That is why sponsorship is so vital.
It is said in "the rooms" that "we keep what we have only by giving it away". To avoid relapse, we need to be aware of what is called "euphoric recall" where you only remember the good and forget the bad. To keep the memories accurate, we need to constantly talk about the problems caused by addiction and to keep from having the same conversations over and over again, newcomers are essential. sponsorship is a two-way street with the newcomer gaining an understanding support group and the sponsor being reminded of the malfeasance of addiction.
Sponsorship is also the next step in collecting responsibilities. It moves the responsibility from the group to another individual who relies on you in a life-or-death sort of way. The stakes are much higher and one is hopefully less likely to lapse on them.
The third and final stage is relapse. Relapse is a part of recovery and if we fail to recognize this, it is only that much more difficult to revisit the idea of recovery. Relapse can happen at any time and with or without reason.
In the end, the twelve steps are one way to treat addiction and it works for a lot of people. I believe that it is better if we try something which is sensible and has been shown to work. That being said the twelve steps do not claim to be a cure, but rather a rocky and dangerous road which leads back to sanity.
"Keep coming back, it works if you work it, so work it because you're worth it."
PS. The higher power I chose was NA itself, this allowed me to avoid the religious aspects while putting my faith in something more than a door-knob.