"They can search for the children."
Translation:Ellos pueden buscar a los niños.
So from this sentence can I assume buscar means "search for" and we have a personal 'a' (it doesn't mean 'for')?
your are correct in that "buscar" = "to look FOR"
the "a" in this sentence is a personal "a" and is not translated into English.
I think the personal a is an 'a' that is inserted for no other reason than that the object of the verb is a person (or more than one person). Sometimes you'll also find it used with an animal that is a pet. The personal 'a' doesn't get translated into English.