First you will need to find who the original copyright owner of the song is. For example one artist's song may have multiple songwriters, and you will need permission from all of the rights holders on any track or piece of music. Once you have deternined who those rights holders are, you can either try and contact them directly, which can prive very difficult, especially if it is a very well known or successful artist. The best way is to find the artist or songwriter's music publisher or collection society, and to contact them enquiring about permission to use the music.
Please be aware you will need to pay some sort of fee if the permission is granted.