How a Windows Developer can most easily get his software to work well 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).

As long as you're not doing anything unusual such as playing around with hardware or poking around in undocumented API calls and data structures, you should be able to run your code under Wine with few or no modifications. Wine has a fairly complete implementation of the public Windows APIs, so if your program plays nice and doesn't mess around, it should just work.

Don't use too much of the windows API! Don't use anything new from Microsoft ;)