No need to buy any recording software, just try the free one first. there is Audacity which you can get from
http://audacity.sourceforge.net/. learn how to use it.
To record you can either hook up your karaoke machine to you soundcard or you may want to do it all within audacity. To hook up your machine to the pc soundcard you may need some kind of cable that will fit at both end. Your sound card will have a 1/8" jack and your machine out may be rca, Get the correct cable.The other way is to rip you cdg to track one of audacity. Play it and record your vocal on track 2. Then add some efx to the vox , mix and mixdown as a wav file. Convert the file to mp3 and make sure the file size is below 3mb.