Sometimes, as in the case of could've and would've , more than one letter has been omitted. This will establish good habits and alert you to the role of the apostrophe. We went to Marmaduke's restaurant for dinner. An area that causes trouble, is with words that end in 's' or 'z' e.g. That's Cornelius's book.
Confusion arises when the apostrophe is used with a plural noun.
At the zoo, the children were most interested in seeing the lions' den. It was the children's turn to wash up. We had coffee at Ermintrude and Marmaduke's mansion. After dinner at Marmaduke's restaurant, we went back to his place for coffee. The bird's feathers were ruffled.