Version Ubuntu 10.04.
First you have to be able to play MP3s and WMAs (or DVDs for that matter). Since this article is about conversion not making them work I will just give you a link to Ubuntu itself which will tell you how to get them working.
Once they're working, it's easy to get them converted. There are probably several ways to do this and a lot of TERMINAL methods but I wanted a mouse point and click solution. So go to APPLICATIONS-->UBUNTU SOFTWARE CENTER and search for LAME. Install LAME by clicking on the INSTALL button. Note this search will return several packages. The one you want is LAME AN MP3 ENCODING LIBRARY (front end). Now search for XCFA. This stands for X Convert File Audio. This search will just return one result. Install XCFA by clicking on the INSTALL button. Close the Software Center your done installing.
To use XCFA to convert from WMA to MP3; first select the FILES TAB (yellow 1 in the pic) then CLICK the IMPORT button (yellow 2) and select your files you wish to convert (use shift and ctrl to select multiple files). CLICK in the FILE DESTINATION box to pick where you want your new MP3 files to go (yellow 3). Next CLICK the RED BOX's under the MP3 column on all the wma files you want to convert (yellow 4). Last, CLICK the APPLY THE CHANGES button at the bottom left (not pictured).
Your now done. The conversion will take some time to complete but you'll see a progression bar to keep you informed.
NOTE: You can install other CODEXs that will allow you to convert to other formats. You can see on mine that I can do WAV, FLAC, WavP, OGG, MPC, and MP3. I can not covert to APE,M4A, or AAC because I do not have those codexs installed.