My daughter decorates fancy cakes--she's taken that Wilton decorating class. Here are her pointers:
First, be sure the cake is absolutely cooled with no residual warmth.
Next, brush off any loose crumbs.
Then, thin part of the icing, and frost the cake with a thin layer of this icing. (It's called a 'crumb icing' for just that reason: it traps any further loose crumbs.)
Allow the crumb icing to set up for a bit, then apply your regular chosen frosting, and you'll have a beautiful finished look with no crumbs, and no cake coming up with the frosting.
Always use a wide spatula to frost a cake, not a table knife. (A frosting spatula has a straight blade that is about an inch wide.)