Apple’s support page tells you how to go about with the instructions.
From the support page on Apple USA,
hold an electrical charge, Apple will replace your iPad for a service
Okay, we got it so it is not free replacement, let us read on
The service costs $99, plus $6.95 shipping. The total cost is $105.95 per unit.
Reading on further…
No. You will receive a replacement iPad that will not contain any
of your personal data. Before you submit your iPad for service, it is
important to sync your iPad with iTunes to back up your contacts,
calendars, email account settings, bookmarks, apps, etc. Apple is not
responsible for the loss of information when servicing your iPad.
In short, if your iPad battery is dead, you have to pay that amount of service charge and you wont get your data restored by them. Luckily, iTunes restoration isn’t that difficult.
Replacement is subjected to Apple’s Terms and Conditions as dead batteries due to accidents, liquid contact do not qualify for this replacement policy.
Note: Price is in US dollars