GoDaddy Bookkeeping organizes data based on a calendar year. That is: January 1 - December 31 is the default calendar, and what all the "yearly" reports are based upon. This means that you don't actually have to DO anything to close the books! You'll still be able to look back at your historical data, but anything that was recorded in 2010 doesn't have any affect on 2011's P&L or other reports.
If for some reason you'd like to actually delete your old data, you'll can do so on a page-by-page basis. Just select all the transactions on the page using the check box at the top, and then delete using the Delete button also at the top.