Purchases are considered final, but you can try the 'report a problem' link to contact iTunes Support and see if they will refund or credit you : http://reportaproblem.apple.com
If the 'report a problem' link doesn't work then you can try contacting iTunes Support via this page : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption.
Apps might be free to download but a lot then allow in-app purchases to be made in them e.g. to unlock extra features and/or levels. To try and stop it happening again you can turn off in-app purchases on the iPad via Settings > General > Restrictions, and you can require your account's password to be entered for all downloads. You can also hide the App Store ('Installing Apps') and iTunes store apps via the Restrictions screen