Q: I bought a new iPhone 4 and I'm trying to connect to the iTunes store and also to download an app from the app store but its prompting for a payment method. Since i don't use a credit card ..i tried to give my debit card details but it displays an error "

Debit cards are no longer accepted as a valid payment method in all countries - from this page :

You may be able to use other payment types in your country, like debit and Maestro cards.

which implies that they are not accepted in all countries, and there have been a number of posts about them being declined.

For it to have a chance of being accepted it needs to be registered to exactly the same name and address (including format and spacing etc) that you have on your iTunes account, and have been issued by a bank in the country where you and your iTunes account are. You could check with the card issuer to see if it's them that are declining it, and if not then try contacting iTunes support and see if they know why it's being declined (buy you might not be able to use a debit card in your country) : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Account Management

If you can't use a debit card then there are instructions on this page for how to create a new account without giving card details, which will give you a 'none' option and allow you to download free items : http://support.apple.com/kb/HT2534 (if you want to use the same email address on the new account then you will need to remove it from your existing account first e.g. by tapping on it in Settings > iTunes & App Store on your phone, the Store > View Account menu option on your computer's iTunes, or via http://appleid.apple.com)