FILE FORMATS HAVE CHANGED SINCE INSTALLING OFFICE 365 TRIAL

You should be able to change the file association if you have only one version of Word installed, but, if, as Doug suggests, there's still some vestige of Word 2013 installed, then Windows will offer it as the default when you use Open With > Choose Program, and the only way around this is to reregister Word 2010 specifically. You can find detailed instructions at http://www.gmayor.com/Document_Not_Found.htm, but if Word 2010 is installed in the default directory, this command line will be what you want:

C:\Program Files (x86)\Microsoft Office\Office12\winword.exe

To use this, press WinKey+R (that is, press the Windows Key on your keyboard together with the R key). This will open the Run box. Paste this command line in and press Enter. You'll see a message box similar to the one below (except it will refer to Office 2010):

When the progress bar completes, you should be back in business.

It sounds like you probably still have the trial version of 2013 installed.

You can remove all traces of that Office installation by downloading the fixit from the following article:

http://support.microsoft.com/kb/2739501

saving it to your computer and then running it.

You will then probably need to repair the Office 2010 installation via the Control Panel or see the article "How to re-register Word when problems crop up opening files” at:

http://www.word.mvps.org/FAQs/AppErrors/ReRegisterWord.htm