This explanation is describing how mindfulness helps to not be obsessed. It may seem complicated, because I am trying to be specific. However, in practice it is extremely simple.  
\*What is obsession?\*  
The action is that your mind holds the internal representation of the object (person) you are obsessed with in focus.   
It idealizes, devalues, has sex with, argues with, talks to, etc etc this mental object, imagines scenarios.  
These are actually 2 different things. The object and the relationship to the object. Two aspects of obsession.  
There are other factors of obsession which I won't get in to, since they aren't needed for this method to be explained.  
\*The method\*  
\*Choose\* to consciously focus on the object.  
(So that it is not an automatic obsession, but now a conscious, manual focus)  
If the mind goes into imagining relationships to the object: gently bring the mind back to only the object.  
As you focus on the object that is held in mind, you may begin to see more clearly what this is. This is a thought.  
Rather than believing in and being caught up in the thought, you eventually take a step back.   
Sort of like post-nut clarity if you will: "What am I doing?" Clarity. You become estranged from the illusion it creates.  
You will see the futility and suffering of the thought, the delusion of it. And your mind will let go of it. Freedom.  
I truly hope this makes sense to those who give it a try. If you do not give it a try, it probably won't make sense. You can't think about doing this, you have to actually do it.  
Also note: one does not do this to actually stop being obsessed. One does this to see clearly what their obsession is. And if you do, your mind will be more likely to let go of it for the moment.  
Also note: the thoughts may come back, apply the method as needed. See what you are doing clearly rather than let it automatically run, and possibly lead to action.