Sit down in a quiet room with your paper and pencil or computer ready. If you are using a computer for typing the lyrics, pull up a word processing document to type. This is helpful if you are listening to music on your computer as you can easily maneuver between the two programs.
Play one line of the song at a time to make sure you keep the words in order. Write down the words you hear the first time through, without worrying about punctuation. Play the line again, and make sure the lyrics are correct. Plug in the headphones if you are having a difficult time hearing the lyrics. Add a comma after the last word sung before the singer takes a breath or pauses. Add a period at the end of a line.
Replay lines as many times as possible to get it right, and make note of any confusing words by writing a few question marks in brackets. The words may become clearer when you are singing the song or in context with the rest of the lyrics.
Make note of the rhythm of the song, while you are re-listening to the song, after transcribing. A song will have a feel to it, and you'll be able to note how many beats are in a measure. There is no scientific way to do this; it's based on what you hear and feel. Based on the tempo you have found, write in the bars for the measures of music.
Add the lyrics to the first verse, below the bars. Then follow this method for the other verses, chorus or bridge. This will help you if you decide to notate the musical notes.