You can't run "wine" by itself, so putting a link to it on your desktop is meaningless. You use wine to run other, windows, programs.
To double-check that wine is installed, open up a terminal and type "which wine". it will probably show return /usr/bin/wine or something like that. Then, you can run a windows program with it by entering "wine /path/to/windows/executable.exe"
Once you have a program running, you can put the command you use into a desktop shortcut so you can run it from there.
This should be enough to get started, but there's a lot more about wine than that. I recommend reading the documentation on the
winehq homepage.
