The Template controls the layout of the editable area of the page.
Design
To change the Template for a page - or associate a template with an orphaned page - go to Design -> Edit -> Template. The following view will be presented:
1. Select either Exact Matches - templates containing same elements as the page - or Close Matches - templates containing the same elements as the page plus others.
2. Click to select the appropriate template, and Publish the page.
Note that that the layout of an existing page - for example, adding an extra Asset element - may be changed via the Structure interface or via the Template itself.