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It is java based. The screenshot is from Ubuntu but I mostly develop on Windows 7. Should run on mac as well but I have a hard time finding macs to test on (but alpha 3 pre 7 which is this version has been tested and should fully work on all macs that run java 5)
How far do you get? Do you see the program window but you can't use it or doesn't it launch at all? Have you tried alpha 3 pre 4 which is more stable?
How to fix in Windows:
Right click on MCSkinEdit.jar, select Open With and select "Select default program" (even though you already can select java in that list). Now select java in that list and select "Always use the selected program". Now it should work if you double click it.
Other operating systems:
Open the terminal client. Write:
cd <The path to the skinedit file, such as /home/name/skinedit>
java -jar MCSkinEdit.jar