Download recording software and install it on your computer. There are several manufacturers who offer free versions of their recording software, and while the free versions don't have all the features of the full, professional versions, they are more than adequate for simple recording procedures like recording vocals. Audacity by Soundforge is a good choice, and it has the advantage of being compatible with both Windows and Mac systems. Once the file is downloaded, follow the on-screen instructions to install it on your computer.
Plug your microphone into an available USB port. You can also use a line-in microphone jack if your microphone doesn't have a USB connector. This jack is usually on the rear panel of a computer, usually next to the headphone jack. A USB microphone will offer a much cleaner signal, so be advised that unless you have a high-end sound card installed on your computer, the sound quality will be a little lacking if you use the line-in method.
Open up the Audacity program. Go to Edit > Preferences and click on the Audio I/O tab. This will allow you to select the speakers you wish to use in the Playback drop-down menu. Below that will be a Recording menu where you can select the microphone and recording input you'll be using. It's important that the correct input is selected in order to make sure that your microphone is enabled. If it's not, your singing won't make it onto the computer's hard drive.
Click on the "Record" button in Audacity to start recording. This button will be marked with a red circle, just like it would if you were recording on an old analog tape deck. Begin singing into the microphone at a distance of around 6 inches or so. As you sing, you'll see a wave form on the screen. This graphic may look intimidating, but it's simply a representation of the sound you are recording.
Click on the "Stop" button when you've finished singing. Hit the "Rewind" button and then hit "Play" to audition your vocal performance. If you're not happy with it, simply repeat the process and record takes until you're satisfied. If you like most of the take and only want to redo a certain section, simply hit the Record button right before the part you want to replace, sing the part, and then hit the Stop button. This is called a "punch-in" and is a common procedure in all recording studios.
Click "Save Project" and give the song a name, saving the file to the CD-RW drive of your computer. Then, insert a blank CD in the CD drive and burn the audio file to the disc. Your vocal performance is now on a CD.