Sugar paste is gumpaste or fondant in the US?? For fondant I wrap it in plastic and then put it in a ziplock plastic bag. For gumpaste, the same thing. You can also freeze these two if it won't be soon that you need them.
Buttercream--Refrigerate, then bring back to room temp and rewhip before using it.
Royal icing--I just cover that with plastic wrap on the surface and leave it at room temp in a sealed container. That's if it's made with pastuerized egg whites. It will break down eventually, so throw it out.
Modeling chocolate- wrap in plastic wrap and keep it in a container for months...If it dries out you can put it in the microwave to soften it up, then knead it with some shortening to get it back into pliable shape. If it gets too old then it will be crumbly and you'll need to throw it out, but it lasts a long time.
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