I was just having this problem until today. It is now all sorted and I can explain what to do very simply and easily.
I remembered the answers to my questions, I just forgot "EXACTLY" how I entered the text - so I had to have them reset. The easiest way is to sign in through www.appleid.com. Then on the right click the "Manage your Account" link and sign in. Easy so far right. Then, as others have said, look on the left of the screen you will see a link called "Password and Security" - click on this. Now this is where the confusion begins. Some people have a link located directly under the existing questions that looks like this "Forgot your answers? Send reset security info email to blah blah blah email. If you see this click it and it will send an email to the "Rescue Email" address that you entered when you originally entered your answers. Follow the instructions contained in this email and you are done. If you cannot remember this email address or you have since closed it, you will need to go to the Itunes Express lane and send an email to Apple requesting them to reset your answers.
HOWEVER IF YOU DO NOT SEE A THIS LINK UNDER THE QUESTIONS - this means that you DID NOT enter a Rescue email address when you originally set your questions. The only way you can now reset your Security Questions and Answers is to go to the Itunes Express lane and email Apple asking to have these reset. I have 2 apple accounts, one for myself and one for my daughter - as I did not include a rescue email I had to email apple. On both occasions, these questions were reset and an email sent to me exactly 24 hours after I sent them the request. I entered the new details, WROTE THEM DOWN EXACTLY AS I ENTERED THEM THIS TIME, entered a Rescue Email this time and I am good to go again. Simple. Now when I log in and click on "Password and Security" I do have the reset link visable. Apple support are good, they just take a bit of time to get things done, but they always seem to get there in the end. I just wish someone had taken the time to explain this somewhere else in the forum as it would have saved me much time and angst.
To get to the Itunes Express Lane go to this website www.appleid.com make sure the correct country is displayed top right, if not change it. Once this is saved go to the tabs at the top of the screen and click Support. Then halfway down the next page you will see a photo of two random people with a title of Contact Apple Support - Click this. Scroll down until you see the itunes logo, to the right of this you will see the link Express Lane for iTunes Player and iTunes Store - click on this. One the right hand side of the next page click on the link "itunes Store". On the next page click the link "Account Management" check the radio button beside "itunes store account security", select your country from the drop down box and click "Continue". Under the heading MORE OPTIONS, you will see a clickable link called email - click this. Fill in your name, Apple ID and country. Then in the text box, write "I have forgotten the answers to my Security questions, would you kindly please reset them. Thank-You". Then Click Continue, you will be given a reference number and an email is sent to your address advising that generally someone will attend to your request within 24 hours. Like I said previously, I had to do this twice and both times it was reset however it was done within about 5 minutes of the 24 hour cut off, so you will have to be patient. I know 100% that this works for Australia - I am guessing other countries should be similar. Hope this helps someone somewhere!
