If you see this message at the top of your store:
This is a demo store. Any orders placed through this store will not be honored or fulfilled.
this means that you have Magento's Demo Store Notice enabled. Displaying this notice is recommended when you are developing your store, but once you are ready to go live and start processing orders, the demo notice should be disabled.
Step 1: go to System > Configuration > Design option in the left menu
Step 2: go to HTML Head. At the bottom of this section you will see the option Display Demo Store Notice.
Step 3: Set this to No and save the change by clicking Save Config.
The demo notice will be removed and you will be able to start accepting orders.
Hope this help!