"František takes care of horses."
Translation:František se stará o koně.
See the Tips and notes and https://en.wikipedia.org/wiki/Czech_word_order#Clitics
It is the first unstressed position after the first stressed unit in the sentence. That unit may consist of several logically connected words.
I think maybe I have figured it out! Is it that "se" has to be second, not first, and not third? ...so if the sentence starts with a person's name, "se" comes before the main part of the verb so that it is second, but if the sentence starts with the main part of the verb, "se" comes after it in order to be second?
Would one of the moderators p lease clarify: in Czech, are there two verbs (starat and starat se), the first one being a "stand alone" verb that means to take care, and the other needing "se" to be used in the sentence - in the second position, of course, that means to care about something? Perhaps I just don't understand what reflexive verbs are... But I'm hopeful! Thanks in advance.
"Starat" is not a valid verb in Czech. Only "starat se": https://cs.wiktionary.org/wiki/starat_se
Many verbs exist in pairs of "stand alone" and reflexive, e.g. "zajímat" and "zajímat se", or "mýt" and "mýt se", but some verbs only exist either as reflexive (e.g. "starat se") or non-reflexive (e.g. "jít").