"She refuses to eat."
Translation:Elle refuse de manger.
In many cases, it is easier to not try to equate it directly to English. "Refuser de" is correct, similar to how "chercher" doesn't require a preposition, but in English "look for" it does. I find that it is easier in a learning sense to accept the language the way it is, because English is far worse in many instances - "had had" for example.
My explanation was not 100%. Each verb that requires a preposition has its own:
Apprendre is on this page: http://french.about.com/cs/grammar/a/verbswithprep.htm
Refuser is on this page: http://french.about.com/cs/grammar/a/verbswithprep_4.htm
It depends on the verb. Some need nothing, some need an 'à' or a 'de' or an 'en' or something else entirely. http://french.about.com/cs/grammar/a/verbswithprep.htm