Depends! Often new systems come with an Office 2010 trial which requires you to buy a key to get full functionality after the 60 days or whatever period.
However if you bought a system which said it had the full version then the vendor should have supplied a key. Have you checked all the bumpf you got when it was delivered? Contact the supplier if you are unsure.
If you don't have a key or can't find one then legally you will need to buy another to use Office I'm afraid. You could try downloading
OpenOffice which is free and offers most of the functions that Office 2010 has...