Patching and Plastering - Fixing cracks in old wall?

We recently bought a house, built 1950's in Tucson, Arizona. One of the walls in the master bedroom has a lot of cracks. The previous owners tried to repair them, but the cracks re-appeared. The wall is not an interior wall, and the cracks appear to be cause by the settling of the house. We cannot tell what the wall is made of (plaster, etc). My questions are: how do we determine what the wall is made of? Should we attempt to repair the cracks ourselves, and if so, what do we have to do? OR should we call in a professional? A friend of ours had a similar experience and just put new drywall up over the existing wall - is that a safe and viable option?

This is third time that the wall crack ? has come up in the past week. I will repeat the repair trick recently told me by a pro painter of 40 years experience. He uses 6"-8" wide strips of black plastic screen "wire", and muds it in exactly like you do sheetrock tape. Says it works great for old plaster walls, etc. and it should work for you. Surely, your settling has stopped by now, and you just need a permanent repair. Good Luck!