Choose a digital microphone and audio software such as Sony's "Soundforge Audio Studio" or "n-Track Studio 6." You can purchase a microphone at a music store. Unless you have a full band at your disposal, purchase backing tracks to sing along with.
Install your audio software and plug your microphone into your computer. Play the background track you plan to sing along with. Record it as a track on its own. This is the track you will open in your audio software to sing along with.
Do another track over the initial audio track. This will be you singing along with the music track. This is the simplest way to record your voice singing at home
Play back the recording and use your audio software's mixing capabilities to adjust the levels of the music track to your vocal track. You want to find the right balance between the two. The vocal should sound crisp and clear without overpowering the music. This is the simplest, most affordable way to record your singing at home, though you will have more control over the mixing process if you have the means to record each instrumental track yourself.