Install Wine from your package manager. Under Debian/Ubuntu it's simple.
apt-get install wine
If you try to run autostumbler with Wine it will complain that you don't have the mono libraries installed. So run over to go-mono.com and download the Windows version with GTK and XSP (about 70megs).
Once the download is finished, run the installer under wine.
wine mono-1.9.1-gtksharp-2.10.4-win32-2.exe
Supposedly Wine doesn't provide some library that autostumbler requires (GDIPlus), so you're going to have to download and extract it into your wine/drive_c/windows/system32 folder (usually hidden under ~/.wine).
After the DLL is extracted, run winecfg and under the "libraries tab" find the gdiplus library and "Add" it.
You should now be able to run AutoStumbler under Linux with Wine!
wine autostumbler1.exe
Input your AS user/pass, stumbler user/pass your URL of choice and hit "AutoStumble" and you should be good to go.
It doesn't appear to like to be minimized, so just don't do it :D. I have a feeling it's still working while it's minimized, but I lose the ability to see what's going on.