Basically a barley twist vase is a hollow form that has been turned with an even wall thickness and then the binds carved into it afterwards.
I firstly use chisels and a lathe to turn a vase or hollow form, depending on the design, from a log of wood. The inside of the vase is turned away through the hole in the top whilst the rest of the form is left as solid wood. Once I've turned the vase I use the indexing ring on the lathe to mark out where I want the binds and also the shape of the binds before using carving tools to carve the wood away in between each bind.
I find it is easiest to mark out the position and curvature of the binds in pencil first before carving since it can be a little tricky working out the optimum shape of the binds that best suits the overall shape of the vase and gives the most ascetically pleasing form.
Once I'm satisfied with the carved binds I then hand sand each one and finish the vase.