To make a new object from a pre-existing one, just change the ID. But that's probably not what you mean.
If you mean to make an entire new texture for a tapestry, the CS cannot do that. You have to create the texture yourself in an Image program, then attach it to a mesh. You can make a new mesh in a 3D rendering program, or use one from Morrowind.
http://www.gimp.org/ is free, and a lot of modders use it to make/edit textures.
Other free tools for making new objects include http://niftools.sourceforge.net/wiki/NifSkope and http://www.blender.org/. (for mesh editing, and texture paths)