Q: How to download apps without a credit card?

If you only want the free apps, take a look here:

http://support.apple.com/kb/HT2534

Read the steps carefully as the order in which you follow them is  critical. Note that you can do this only when creating a new Apple ID. You cannot use an existing ID. 

You will of course not be able to get anything other than the free apps without entering in some sort of payment method (credit card, prepaid iTunes card, gift certificate, etc.)

Regards.

Forum Tip: Since you're new here, you've probably not discovered the Search feature available on every Communities page, but next time, it might save you time (and everyone else from having to answer the same question multiple times) if you search a couple of ways for a topic, both in the relevant forums and in the Apple Knowledge Base, before you post a question.

If you want to create a new account without giving credit card details then follow the instructions on this page when creating the account : http://support.apple.com/kb/HT2534

If you don't use those instructions when creating an account then card details will need to be entered before the account can be used to download any item from the store