Young Il Kim
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Although this tutorial is about making vases, it applies equally well to making tumblers.  First create a template by wrapping a stiff material around the glass and trimming it to size.  Roofing paper works well for making templates for clay handbuilding. Building it over the original glass helps to hold the structure.  Baby power can be used instead of a non-stick liquid to help the clay to slide off.  Don't forget to add a bottom.

create template by wrapping stiff material round the glass & trim to size. Building it over the original glass helps to hold the structure. Baby powder instead of non-stick liquid to help the clay slide off. Add a bottom!