I would like to have spiral shape texture on the cylinder. How to UV map the model and how to make a texture which wraps around the cylinder ?
First, unwrap your cylinder -- Edit Mode; Select all (A); Unwrap (U) -- with a cylindrical projection. Use a texture that joins the top and the bottom seamlessly.
Then select the bottom row in the UV window (B and make a rectangle) and shear it by grabbing to a side (G).