Need tutorial on how to make a headband for my Sim.

Your best way would probably be to first clone the hair you want to use it on and then design your mesh so it fits that hair. Then join your band to the hair mesh, weight it completely to the head, and vertex paint it to match the hair's vertex paint. Alternatively you could make it as an accessory but it certainly won't fit all the hairs if you go that route.

I think you would need to make it as a mesh that was mapped directly over the part of the hair that it will lie over in the game. I can't tell without looking at the actual mesh how the hair is mapped but that would be the optimal way of going about this I think if you could do it without remapping the hair.  Alternatively you could shrink the hair image and map a small amount to buy yourself some space in that corner to map your headband.  It might be easier to do it as an accessory but you would end up having a fairly tiny area to work with in mapping your new item that way.