Ира Родила Девчонку, Велела Тащить Пеленку. :)
Easy? My son studies it in school, and it often gets hard even for him, though he's a native russian :))
Maybe just... check and note the corresponding questions (кто, что? кого, кому, о ком? и т.д.)
But my advice would be just drop it for a while at all, means don't care about the cases - better remember the "use cases" or collocations (if I call it right). I assure you, good half of us are not good with this stuff from this academical point of view, but anyone can use it correctly while speaking.