Contact the artist and/or record company whose music will be used in the video.
Obtain written permission to use the music in the video. A simple verbal agreement might not hold up in court if the mind of the artist is changed later. For signed artists, the record company owns the rights to the music and will need to give its permission.
Ask the rights holders (artist, record company) how they want to be cited. Generally the artist's name, song title, release date and record company's name will be used. This information is often displayed in a small graphic on the lower portion of the screen. The information might appear at the start and end of the video or be displayed throughout. At the end of the video, this information might be more prominently displayed in the credits along with a thank you for the use of the song.