Skill songs are a purchasable perk in the "skills" section of the skill shop. They are normal songs on the in-game radio stations that double your skill multiplier for their duration. They only occur in freeroam. To "take part" in one, perform a skill while one is playing (the DJ will announce when they are playing one, and the multiplier should be purple during it) and bank the points.
I'm not entirely sure how often they play but I would estimate one every hour, however you can reduce this to around one every half hour by buying the "radio star" perk, which is two up, one right from the first skill song perk.JordanBelfort87
points out Groove Music does not have skill songs.ZRkillerBUSH
notes disabling the radio DJs in the audio settings also disables skill songs, don't do this.