Since I've been getting on Mudcat I've been finding out that a lot of songs that I've heard that I thought were by the original artist are actually covers. For example, Led Zeppelin taking the writing credits for "Nobody's Fault But Mine" (among many others) or Fairport Convention attributing "Open the Door Richard" to Bob Dylan.

My question is, how do you determine who gets writing credit for a song? Can an artist take and existing song, change a couple minor things, and then take credit for writing it?