I may not be right person to tell the correct procedure but I have read selected parts of this book as per advice from one of the old time Orkut communities for Algorithms. Though I don't consider myself good at algorithms, I believe this book was instrumental to my understanding of algorithms and analysis. CLRS is a book with large coverage on all main topics in Algorithms and is hard to be read as a prescribed text in algorithms course. To be frank, my main motivation for reading this book was to get through big interviews like MS, Google etc.I had an internship interview with Microsoft. I was not so confident but I made it to the final round. At that point of time, I was not so comfortable with algorithmic design techniques. I did not clear the interview. Then I started reading this book in my junior year. As I read through I was able to point out and say that this chapter was important for me to read. I tried to solve the problems given in the exercises or tried to look for solutions from communities in Orkut. (There was a community to discuss questions in CLRS). I made sure that I solved every problem in the chapters that I read. I have highlighted the parts that I read below. I am not saying that this is the correct way to proceed but I felt that my selection of chapters was enough to do well in interviews. Please note that this is my specific case and I am not claiming that reading the highlighted portion will help you crack any interview :)It is also important to note that it is good to solve all the problems in the highlighted chapters than just reading the content.My answer is mainly aligned with interview preparation than competitive programming but I still believe this selection will be the later's subset.