As xJuliet said, I do the exact same. I listen to the song and then I look at the lyrics whilst listening to the song and keeping track of how they go. I do it bit by bit until I have a part completely perfect. I then move onto the next part then do a final runthrough. For example, I do the first verse until the end of the first chorus. Repeat and repeat until I feel comfortable enough to move onto the next part of the song. By the time you learn it, you will have memorized particular parts of the song and it saves you concentrating so hard on the lyrics that you have no emotion in your voice.