A trick to using the verb Chiedere properly.
Early on in the Present Tense verbs, we are instructed that the verb Chiedere means "To ask".
And so we get a sentence to translate:
She asks for an apple.
Using our ingrained English stubborness, we see that sentence and write,
"Lei chiede per una mela."
And that is incorrect. "What?!", we exclaim. "That's crazy! Where's the "per" in the answer?"
After getting it wrong, the first dozen times, we amend that initial lesson and now think about "Chiedere" as really meaning, "To ask for".
Because the correct Italian translation for, "She asks for an apple", is actually:
Lei chiede una mela.
Now here's the trick.
Much like "Aspettare" (to wait "for"), the word "for" is already implied with "Chiedere". And so instead of using "To Wait" for aspettare, I suggested previously that you instead think to use the word "await", and that way you'll never need the word "for".
Example: "Io aspetto il treno". "I await the train". (I wait for the train).
It's taken me weeks, thinking about this, but I finally just realized what the "correct" translation of "Chiedere" should be. It isn't "to ask for"; although that works just fine during translation exercises.
Instead, try to think of Chiedere as "To request".
She requests an apple. Lei chiede una mela.
That troublesome word "for" is no longer an issue, and you are not going to add "per" into your sentences after chiede, now.
Because you would never say, "She requests for an apple".
Even English stubborness isn't going to make you add the extra word to that sentence.
Great suggestion Mabby. Infact, I wouldn't be surprised to find out that there is some kind of etymological connection between chiedere and request
Thanks a lot!
EDIT: Just looked it up, sure enough there is. both come from "quaerere"
You are right, "chiedere" could also mean "to pose a question to someone" or "to ask for an explanation", and in this occurrence the verb is followed by one of the prepositions "a-ad-al-alla-allo-ai-alle-agli". That's not an idiomatic sentence, it's pure Italian grammar! :) You need the preposition "a" because you are introducing "complemento di termine", which is a type of indirect complement who specifies to whom or what is directed the action that the verb express. In "Chiedo una mela" there is no need to use a preposition because "una mela" is the direct object ("complemento oggetto") of predicate "chiedere", but you will need a preposition and a "complemento di termine" for stating to what person/people you are requesting an apple: "Chiedo una mela al professore". In "chiedo al professore" the direct object (a question, an explanation) is implied.
Other meanings of "chiedere" are "to ask after someone" or "to desire to talk to (or meet) someone". In these instances the verb is followed by preposition "di". eg "I tuoi genitori chiedono di te" --> "Your parents are asking after you"; "Degli uomini chiedono di lei alla porta" --> "Some men are at the door and want to talk to (or meet) her". "Di lei" and "di te" are also indirect complements, this time "complementi di specificazione": they make more specific the meaning of the word they depend on (chiedere, here). These meanings of "chiedere" are not very common, though.
tl;dr: when "chiedere" concerns something you don't use a preposition, instead when it concerns someone you use "a" when you want to pose a question to someone, or "di" when you want to talk with someone or hear some news from him/her.
Hope this will help and forgive me if I made some mistakes, English is not my mother language.
Yes, there are quite a few little idiomatic sentences in Italian like that one.
Many Italians would prefer to use the verb "fare" when talking about a question:
Lei fa una domanda al professore.
It can't make sense unless you've just said it that way, all your life.
Sort of like in English, when someone is "under arrest"-- why "under"? Because that's the way you say it.
You could think of it as asking for information if that helps. "Chiedere" isn't used with "domanda," as Mabby pointed out, but you can use it with the question itself:
Mi ha chiesto dov'era il gatto. He asked me where the cat was.
Mi ha chiesto: "Dov'è il gatto?" He asked me, "Where is the cat?"
When you ask for something you need an object, "Lei chiede una mela" really means that she wants the person she's speaking to to give her an apple. When you are asking a question in Italian then you don't use the verb Chiedere + object because that would mean that you are requesting it, you are instead asking something (an answer) of someone, which in Italian takes the dative case, which is represented with the "a" in "chiedere a".
 I just noticed that this question had already been answered to an even fuller exent, so my bad I guess.
I've been reading this discussion. In order to say 'I ask the professor for an apple', would I say 'chiedo un mela al professore'?
Una mela... yours might work but I would probably say 'Chiedo il professore (la prfessoressa) per una mela.'
I think that you have to swap the subject and the noun:
Chiedo al professore una mela.
I'm not certain but "Chiedo un mela dal professore." might work; "I request an apple from the professor".
And so instead of using "To Wait" for aspettare, I suggested previously that you instead think to use the word "await", and that way you'll never need the word "for".
I remember when you posted that tip, I do now mentally translate 'aspettare' to 'to await' and it's very helpful!