The cake should be cooling on a rack, with air circulating on all sides.
When the cake is fully cool (about 2 hours), move it to its cakeboard. If this is a layer cake, now is when you pipe a dam and apply the filling, then stack the layers.
Apply a crumbcoat. This is a very thin layer of the same buttercream you will later frost the cake with. It doesn't have to be pretty -- it won't show. It seals the cake for freshness and also glues any loose crumbs to the cake so they don't show up in the final frosting.
All the crumbcoat to dry.
Now you can proceed to frost and decorate, or you can wait. If this is a filled layer cake it is best if possible to allow the layers to settle a few hours before frosting. If it is a single layer then it is just up to what fits your schedule best.
Unless the cake has a perishable filling (cream cheese, pudding, custard, mousse, etc.), it is best to let the cake sit at room temperature. To protect it against dust, pet hair, etc., cover it loosely with a clean dishtowel or place it in a cake box. (If you also need to protect it from inquisitive little fingers or paws, put the box out of reach.) Do not use an airtight container.
If the cake does have a perishable filling (which I try to avoid, because it is a hassle), then it needs to be refrigerated before and after you frost and decorate it.
Does this help? Good luck with your cake!
(By the way, did you realize you posted in the wedding forum?)
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