Many of my users have been telling me that they'd like to run my software on their Linux machines under Wine.
But I'm a Windows Developer who has practically no experience with Linux.
Now I could spend a month or two installing Linux, learning Linux, installing Wine, learning Wine, and thoroughly ensure my application runs well under Wine. But I am still developing for Windows, so I don't want to take so much time away from development right now.
So what can I do without too much effort to get my program running as well as possible under Wine?
I did find this General help on running applications under Wine.
Download VMWare and an Ubuntu virtual machine (Ubuntu is a popular Linux distribution) from the VMWare site. This will provide you with a working Linux O/S inside your Windows environment without needing to install Linux manually.
You can then use the instructions here to install Wine, that Wiki page also provides you with some instructions on how to use it.
If you follow what Adam Rosenfield suggested and just try running your application in Wine unmodified, you will be able to determine quickly whether there are problems. My guess would be that there are some, otherwise your users would not have contacted you about it :)
There are many ways for getting help with debugging applications in Wine, consult the website for options and pick a few ways that suit you. As always, it's best not to rely on a single channel for communication.
Also, if you are more comfortable with developing in Windows, the approach of using a virtual machine will allow you to compile your code as usual in Windows and copy the binary into the virtual machine for testing (Ubuntu supports browsing/mounting Windows shares).