Hola Felix

It is a tricky one, so I'm sure you are not the only one...

We use tratar "de".. when we talk about a "topic", for example in "la película trata de la Guerra Civil española". This is normally translated as "to be about..." and that "de" would be "about". 

When we use the verb on its own without de, the meaning is different and also the context. It means "to treat", as in treating an illness, or treating a person badly or well, for example. Tratar is also used in a very similar way to tratar de as in being about (as explained before) and this distinction is quite difficult to explain and see and could be the most problematic bit. I´ll give you these two sentences that look very similar but are different semantically:

1. La conferencia trató el problema de la influencia de la tecnología en los adolescentes.

2. La conferencia trataba de la influencia de la tecnología en los adolescentes.

In number one, the meaning of that tratar is "addressed , touched on". That wasn't the only topic of the conference, but they did touch on that specific topic (among others).

In number two, the meaning of tratar de is "was about", so here, we are talking about the actual theme of the conference, the whole conference was about that theme. 

It is a different nuance that is difficult to see as it's using the same verb and the meaning is very similar. 

I hope this helped clarify it a bit more.

Saludos cordiales

Inma