This is the recipe I use - there are many others out there but this one works for me.
250g plain flour
1/4 teaspoon salt
1/4 teaspoon baking powder
100g caster sugar
(preheat oven to 170)
Sift together the flour, salt and baking powder.
In another bowl mix the butter and sugar until they're sort of frothy.
Combine the frothy mix with the flour mixture to form a dough. If it gets awfully warm you can chill it for 10 minutes.
Roll out to about 1cm or thereabouts thick and either use cutters to make nice shapes or what I do is push it into a mould I have of a thistle! It's actually a butter mould but it works fine for shortbread - a light dusting of icing sugar stops it sticking.
Cook for 25 minutes. ( I find that recipes will say to cook for a lot less time than this - but when I try for less they're never cooked)