Can Anyone Tell Me How To Polish Seashells So As To To Make Them Shiny And Attractive?

Mineral oil, in most cases.  Rub in gently with a soft cloth.  Baby oil, that kind of thing, is perfect.  Leave it to soak in for a few hours than wipe off.

Don't use vegetable oil or anything organic; it will go smelly.

Some shells will stay shiny with rare polishing, others need it almost weekly, depends how often they're handled.

Cheap way to do this is to spray WD40 (or similar light motor oil) on.  This comes off easily and smells, though.

You can spray the shell with a sealing spray afterwards, but this may flake off over time.

Make sure that the shell is extremely clean before you start. Rinsed with water. Then soaked in disinfectant to kill any remaining life forms and/or render their residue non-smelly.  You can use extra saline solution to disinfectant, or a 50-50 mix of water chlorine, or even put the shell in very hot (but not boiling) pot of water for 20 minutes.  Then rinsed again and left to thoroughly dry.