When you open a document from a previous version, you can see [Compatibility Mode] in the title bar.
To convert the document, click on the Microsoft Office button in the left hand corner, and then click on Convert.
You should be prompted to save the converted document to a new filename.
Once the document is saved, now you’ll need to close the current one and reopen the converted document. Thankfully there’s a ridiculously wide dialog window that will let you do that automatically.
You can see that the new window doesn’t say “[Compatibility Mode]” in the title bar anymore.