How do you store scotch whiskey with cork?

Scotch whiskey (no e for scotch), and all other whiskeys for that matter are light and oxygen sensitive. Exposure to either will degrade flavour and odour, so keep the stopper on at all times when not pouring. Keep the bottle in the box it came in (and if it didn't have a box buy a different malt next time) and keep the box in a cool, dark, dry area.

As for the orientation, while wines that have cork stoppers in them must keep the cork moist in order to keep the seal viable, as far as I am aware whiskys do not have this problem. Although I have occasionally come across a bottle with a disintegrating cork that had seen better days, I am fairly certain that the cork would have imparted unpleasant flavours into the whiskey had it been kept on its side.

In summary, keep away from light, keep the stopper on whenever possible, and keep the bottle upright. Basically the way you see them displayed at the bottle shop.