Hi Laura,
in fact it is guided by grammatical rules. If I am correct, it is called a 'Fakultativ' and it can refer to a subject in 3rd person or a complete subsentence. I would say it is used to emphasize the subject a bit more.
Let's take your example:
"Es befinden sich Kreise auf ihm"
could also be said 'regularly' as:
"Kreise befinden sich auf ihm"
or putting the object to the 1st position:
"Auf ihm befinden sich Kreise"
If however you want to emphasize the "Kreise" even more, you can use that Fakultativ. you simply add it to the sentence, put it to the 1st position and arrange the rest accordingly (namely the subject goes to the position after the verb):
"Es befinden sich Kreise auf ihm"
Just remember: If you use the "Es" as Fakultativ as it's done here, it has to be on the first position, otherwise it doesn't work. That doesn't apply to the "Es" as pronoun, of course.
If you ask me, if there is a rule to know -when- to use it, I couldn't formulate one. It's - as often - a matter of feeling about the language. However, pointing out a subjet could be a possibility. The sound of it is mostly formal, sometimes even a bit artificial.
"Die Frau trinkt." could be put to:
"Es trinkt die Frau" which sounds like a sophisticated, artificial way to speak, which sometimes can be fitting (thinking of poems, e. g.)
As for the case with the complete subsentence:
"Dass du traurig bist, tut mir leid."
something like "I'm sorry for you being sad."
or:
"Es tut mir leid, dass du traurig bist."
Here the "Es is referring to the complete subsentence, i. e. the fact that "you are sad"
Hope I could help. If you have any further questions, don't hesitate to ask, and I will try to explain a bit more understandable! ;)
Daniel
P. S. Whoa, now I see, I didn't answer in the correct post, I guess. Hope this still finds you. :)