What recording equiment do I need to participate? Any Suggestions?
It doesn't have to be the 'abbey roads' studio! (No problem if it is ...)
OK, most basic, you'll either need a microphone or the line out of your instrument or amp.
Now theres the question of how to get the signal into your computer... You may try what happens if you put your mic/line into your onboard soundcards mini-jacks (you'll need to have some adaptors from big to small then), but lets be honest: that will not sound good in most cases, for regular onboard hifi sound cards are not designed to handle instrument signals or work well with good microphones. Lets not go into technichal detail too far.
If you are looking for a simple solution, look out for a so called USB Audio interface - thant would be a little box with proper instrument-sized mic/line in jack with maybe a preamp-gain knob to set the levels, wich you may easily hook up to your computer by good old USB.
Next you'll need a software to record the incoming signal and mix it with the backing track of your choice. Audacity & Reaper have been recommended as good freeware tips to google for.
Last, you'll have to convert your remix to 320k-mp3 or 192k-mp3 file format (Audacity can do this right away) of less than 15 MB filesize.
If you have more specific questions on how to record your instrument, feel free to ask in one of the community boards!