Do we have to enter our card details when making a apple account?

I'm making a account on my iPhone. There's no option where we can't enter our card details

Yes there's, there's a small skip button somewhere (If I can recall it correctly.)

Depend on your country, there are some tutorial guide how to create an Apple account without credit card but it's not easy to set up, if you don't want to waste time, just request someone in Fiverr help you
something like this:
http://fiverr.com/apple_review/create-one-apple-account-any-country-without-credit-card

No you don't. I have never associated a credit card with Apple. Try making an Apple account from the Mail app or the Find My Friends app, rather than the Itunes or app store apps. Hope this helps!