First, make sure you have a computer available with a CD burner. You can use either a laptop or a desktop.
Get CD's that can be written to. This will be the CD-RW. You can then write to the CD, and also change it later if necessary.
Next, set up an account with an online company that sell Karaoke music. I have put a few in the additional resources portion of this page.
After you set-up your account, you can browse the music choices and purchase only the music you want. It will then download to your computer through a program installed by the music provider.
Via your CD burner, you can now burn which songs you would like to your CD. The burner will walk you through the steps required to pick, burn, and finalize the CD.
Using a karaoke machine or cd player, enjoy your music.