The book Effective Java and other sources provide a pretty good explanation on how and when to use the readObject() method when working with serializable Java class
Item 90, Effective Java, 3rd Ed covers readResolve and writeReplace for serial proxies - their main use. The examples do not write out readObject and writeObject methods because they are using default serialisation to read and write fields.
readResolve is called after readObject has returned (conversely writeReplace is called before writeObject and probably on a different object). The object the method returns replaces this object returned to the user of ObjectInputStream.readObject and any further back references to the object in the stream. Both readResolve and writeReplace may return objects of the same or different types. Returning the same type is useful in some cases where fields must be final and either backward compatibility is required or values must copied and/or validated.
Use of readResolve does not enforce the singleton property.