What can I do for my new ipad with its screen broken. And I bought it four month ago.

If by "broken" you mean that the screen is physically damaged due to accident or abuse, then no, Apple will not service it for free. If you have AppleCare+ for the iPad, Apple will replace it for the AppleCare+ fee standard for the plan in your country; it's $49 in the US.

Otherwise, Apple does not repair iPads, but will replace the entire iPad for their flat out-of-warranty replacement fee; see the Repair Pricing section here:

http://www.apple.com/support/ipad/service/faq/

There are independent iPad repair services that may be able to replace the screen for less. Do a web search for "ipad repair". Note, though, that if you elect to have the iPad serviced by an unauthorized shop, all further warranty will be void.

Regards.