Attach your microphone and headphones to your computer. Most computers have two quarter-inch jack inputs, one for a microphone and one for headphones. You may need to purchase a converter piece to plug your equipment into your computer.
Open Audacity. Click the "File" tab at the top of the screen and choose "Open" from the drop-down menu. Locate the instrumental track that you wish to record vocals over and open that file.
Click the "Tracks" tab at the top of the screen. Float your mouse over the "Add New" button and choose "Audio Track" from the menu that appears.
Put the headphones on and click the record button (the red circle button at the top of the screen). Sing or talk into the microphone to record your voice. Click the stop button (the square yellow button at the top of the screen).
Repeat steps 2 through 4 if you want to add multiple vocal tracks.