Update For those that don't mind adding PPA's, packages are now available here for 14.04 & 14.10

PPSSPP has a Linux version. The instructions provided only work with the 64 bit version and you have to build the 32bit version yourself, although there is a promise that a .deb for Ubuntu/Debian users is on the way

Download the tar.gz from here

Extract to a place of your choice
You can now launch the application by double clicking the executable.

To create a launcher and make it searchable from the dash:

If you don't already have it installed then open Software Centre, search for and install 'Main Menu'

Open 'Main Menu' from the dash

Select a category where you would like to place your application (for this purpose I have selected 'games')

Click on new item, give your launcher a name i.e PPSSPP then in the command box click browse, navigate to the executable you have for PPSSPP, click open

At this point you can just click OK and your launcher will be created, however there is also the option to to give your launcher an icon (unfortunately no icons are included in the download)

To change the icon click on the 'springboard like logo to the left

you will then be able to select a logo from file or if you have your own navigate to that and select.
If you don't choose a different icon it will just default to the springboard.