There are different type of reconstructing memory: recall, recollection, recognition and relearning.
recalling is getting access to our memory storage in our brain. For example, on the day when taking exam, students have to recall the memory that they have studied. Recollection is different type of reconstructing memory. It is organizing the fact or information based on what we recall. It also happen in writing essay. Recognition is the identifying the information based on previous information. For example, when we are trying to answer the multiple choice questions, sometime we eliminate the all the wrong answer to pick the right answer. Relerning is the of memory retrieval involves relearning information that has been previously learned. This often makes it easier to remember and retrieve information in the future and can improve the strength of memory.
The author says that reconstruction memory is not working perfectly everytime. For example there are when people know but could not quite remember something, called "tip of the tongue experience"
To improve the reconstructing memory there are ten ways to improve it in this site. http://psychology.about.com/od/cognitivepsychology/tp/memory_tips.htm