Most Helpful Guy
I am sadly not 100% sure about Youtube. I made a cover myself, put it on youtube and it got flagged. But I can tell you how it woks in the record industry.
It is not the artist that gives the permission. It is done by the people that wrote the song or by the publisher that acts on behalf of the writers. For example Universal Music Publishing. They will send you a document to fill out. What they really want to know is if you will sell this or not. If they are satisfied with what they will see they will grant you permission or ask you to obtain (i believe) a mechanical licence.
It is not as overwhelming as I make it sound. But it is annoying that you have to do this. Also everyday I see people on youtube do this without any permission and be fine. But... you asked... i told you.
Most Helpful Girl
What kind of songs are you talking about?
The songs that are from famous people that do it for money? Then you don't need to, you just need to mention that it's a cover (unless you want to sell your cover, then you need to contact the agency). If it's a non famous person's song, you just ask him/her in the comments section and mention that you will mention that it's a cover of their song.