When working on this essay, the first thing you'll need to do is decide which position you will want to take: either that a singer-songwriter should be able to win the Nobel Prize in literature or not. If, for example, you chose to argue that a songwriter should be eligible for the Nobel Prize in literature, you would state that as your thesis and then go on to back it up with specific evidence. For example, you could argue that he should because composing songs is an art form like literature, and lyrics are like poems.
After coming up with a few specific arguments to support your position (not just the one I made above—that is an example; you'll need to think about it yourself and then make your points and back them up), it's also a good idea to address potential objections. For example, you could say that some might argue that giving the prize to a successful musician like Bob Dylan could make the award more commercial. However, plenty of novelists and poets are also pop culture figures. One could also argue that it's a slippery slope, and once you begin awarding this prize to musicians, where does it stop? Should they have a separate prize for music? In addressing that objection, you could cite some quotes about how unique Mr. Dylan is and what a particular icon he has been in terms of his lyricism, not just his music.