Before you can get started with creating project templates so that they can be packaged into a VSIX project, you will need to install the Visual Studio 2013 SDK which can be downloaded from here: http://www.microsoft.com/en-us/download/details.aspx?id=40758
Once you have done that, you can follow the instructions to export a project template here: http://msdn.microsoft.com/en-us/library/xkh1wxd8.aspx
Finally, you can then proceed with packaging your Project Template by following the instructions in this article: http://msdn.microsoft.com/en-us/library/dd885241.aspx
If you wish to construct a nested Project Template path for your VSIX project, you need to re-create the appropriate folder structure in your VSIX project (you need to emulate the same folder structure that Visual Studio uses as found in this path: C:\Program Files (x86)\Microsoft Visual Studio 12.0\Common7\IDE\ProjectTemplates)
Then, when you install the VSIX package, it should appear in the structure you created as follows: