You’ll need to download and install just three applications to play and convert Windows WMA music files on the Mac.
Your Mac, as it comes straight out of the box, will not be able to play Windows WMA music files. The Quicktime player and iTunes won’t work, not without downloading additional media components.
The first application: VLC
If you just want a fuss-free way to play WMA files on your Mac, download and install the VLC media player.
That’s it. VLC can play the files without any further tweaking or having to install additional codecs. This is how the WMA file icons will look like in the Finder:

This is a screen capture of VLC playing a WMA file:

The drawback to this approach is you cannot add the file to your iTunes library. Nor can you play it in QuickTime if that’s your preferred media player.
Let’s move on to the next application …
The second application: Windows Media® Components for QuickTime
You can play WMA files with the QuickTime player if you download this set of components. Go here, read what it’s all about, and install the package.

Once the package has been installed, you’ll see the Flip4Mac folder in the Applications directory:

Notice that there’s now a WMV Player. The context menu for a WMA file will now show this player to be the default:

Choosing WMV Player will then launch QuickTime to play the file:

At this juncture, you still won’t be able to add the files to your iTunes library. We’ll now have to summon the services of the third application.
The third application: Switch
Switch for the Mac is a free audio / music file conversion software for the Mac (there’s a version for Windows too) that can convert between various formats.

The first time I ran it to convert the WMA files to MP3 (which can then be copied into my iTunes library), the application prompted me to install the Windows Media Components for QuickTime mentioned previously.
Once you have installed those components, Switch will then be able to convert the files without a hitch.
The interface is fairly simple. You just drag and drop an entire folder, or a bunch of files from the Finder into Switch:

Then, select the destination folder. I just check the “Output to same folder as source files” option box. For output formats, you have a ton of options (AIFF, FLAC, OGG, WAV). In my case, I just select MP3.
Click on the Encoder Options button and choose your bitrate. I just go with Constant Bitrate (CBR) at 256 kbps and check the Higher Quality option:

When you’re ready, click on the Convert button, and go for a stretch or grab some coffee as the process takes a while. When it’s complete, just drag your freshly-minted MP3 files into iTunes.