After installing Linux Mint 13 on your machine for the first time, you will only have few to no icons on the desktop by default. This makes accessing important files fast a chore. However, you can change this just like in the present versions of MS Windows.
To do so, go to Menu > Preferences > Cinnamon Settings > Desktop.
Here, tick all the boxes whose items you want to have on the desktop and close the preferences window again. If you want to remove them again, just repeat the process and untick the boxes again.
The usual thing you find when you right-click your desktop to create a new document is the option to create an empty text document. This selection can be widened however by using the Templates folder in your home folder. Any document that is put in there will be selectable; this is also possible with pictures and other formats. Pinguy OS for example provides and excellent working system out of the box and comes with multiple file templates installed:
The string Untitled is put in front every newly created document from a template. To remove an item from the list, just remove it from your Templates folder. By making a document invisible in the Templates folder it is also removed from the list.