You need to select the template as an allowed template type for the Document Type of your pages. Lets say you're page Document Type is called "ContentPage" and you've added a new template called "NewTemplate".
By default you won't be able to select the new template when editing your "ContentPage" pages. You'll need to go into "Settings" in Umbraco, and then expand the "Document Types" folder. You'll see a list of all of the Document Types, select the one you want to use the template on ("ContentPage" in this example).
The first tab that you'll see is the "Info" tab. There's a checkbox list called "Allowed Templates" that you need to select your new template in. Save the Document Type and go back into the Content. You should now be able to select "NewTemplate" as a template on your "ContentPage" pages on the site!