"Her hat"

Translation: O chapéu dela

[connal]

This gets me so often - I get confused about when it is necessary to put the article in front of a noun and when it is not. Is there any guiding rule?

[Paulenrique]

as in English, it's a hard point. But in Portuguese it is much more common than in English! in this case, for instance, when you have dele(s) / dela(s), you have to use the article.