You need to begin by getting some software like Sony Soundforge, or Adobe Audition. Both of these are available in 'trial' versions, which can be, *cough* 'modified', if you know where to look. ;)
Then you need to decide on which track you want to mix, and what you want to do with it. I find it easier to mix the songs I am most familiar with, and it helps to have alternative versions, demos, split channel sources (i.e. DVD-A), from which to add bits to your mix. Personally, I like to try to keep the format of the song virtually intact, and just try to enhance or rearrange parts of it, so that it sounds a little different to the original, and perhaps brings an alternative 'feel' to the song, as in my Play The Game, with the slightly trippy, dreamy effects in the first verse.
It takes a while to get to grips with the software, and the most important thing is that YOU like what you have created - sod everyone else! Another tip is, don't start anything when you are limited for time. Sometimes it can take an hour or two just to get one edit right (well, it does me!), and it can be really frustrating, but you can usually tell straight away if something is going to work or not.
Hope that's a help!
Remember to deliver with the speed of light
A little bit of love and joy