You must always credit the person who created the song. If you are using the music and lyrics of a song, you should include the name of the composer and lyricist.
For example, if you include a song on your website, the credit might read:
Composed by Daisy Bell, Lyrics by Jed Waters.
Sometimes one person will be both the composer and lyricist.
It is also a good idea to acknowledge the copyright owner in the song and the recording of the song (if you are using a recording of the song, such as an MP3 file).
If copyright in the song is owned by Zen Publishing, and copyright in the recording is owned by Wailing Records, and you have obtained permission from both Zen Publishing and Wailing Records to use the song, the credit might look like this: