This is something I put together once when a friend asked for advice on how to study Life and Death. These are unedited comments so if you see anything wrong please let me know. This is my advice for any tesuji, L&D or problem book.
Find a book at a level where you think you can understand EVERY diagram in the book with a little effort. For most people a good starting point is Davis's book on Life & Death but any other at about the same level is good. Choose a book which is more encyclopedic than problem oriented.
If you have not already read the book, do not do so. Instead, turn the book upside down -- to avoid a temptation to read it while looking at the diagrams (if you read upside down then turn it sideways) -- and go through every diagram and see how many you can solve or understand on sight. Then go through again and see how many you can solve inside one minute. Don't count -- just get a feel for the approximate percentages. These are the benchmarks by which to judge progress.
Your ultimate goal is to be able to solve every problem in the book on sight -- no thinking, just hardwire the brain. It take quite a bit of practice, but not as long as you would think provided you practice the positions in your games. As you go through each chapter go out of your way to find and play these positions in your own games, even if it means playing a globally bad move. Encounter the local situations as often as you can. If you are concerned about your rating then play free games because you will lose a lot of games because you are playing locally and not globally.
Do NOT commit sequences to memory -- that is a waste of energy. Just remember that "the L group with no leg is dead, two legs is alive, and one leg is sente." If you know that at first glance then I consider it solved. Note that, remembering this automatically tells you how to kill the Leg+1 group -- play hane to reduce it to the L+0 group. It is as easy as that -- no thinking unless there are peripheral stones around which affect the position. But don't worry about those at first -- just learn the basic shapes. If you play that hane in a game and someone tries to live you know it is dead and can figure it out in the game. The door group is another good shape to use this technique on. It comes up more frequently than most people realize.
The next think to do is to go through the book repeatedly until you can solve or understand EVERY diagram on sight. When you have done that turn it upside down and repeat the process -- just to ensure that you are not remembering the exact diagram on the page instead of understanding the problem for itself. Then repeat the process again with the pages turned sideways. Get to see the problme from every angle so you will instantly recognize them when they occur anywhere.
At this stage you have mastered all the basic shapes and can instantly recognize them whenever they occur in a game. The problem is that in games the complete shapes rarely actually occur. Most shapes are incomplete. So the next step in the instant recognition process is to take each basic shape and, either mentally or, preferably, on the board, lay it out and then remove each stone in the pattern in turn. This gives a new shape and you should work out what this shape means. Is the stone removed critical? Can it be played elsewhere in the shape to greater effect? If the stone removed is from a living shape can the new shape be killed and if so in how many ways? If the stone remove was one of the killing stones is the shape now alive? Learn which are the "most critical" stone to kill or life. Often you will find that not all the stones are actually needed from the problem diagram, only that the shape is losely surrounded. At other times you will find that every stone is critical. Once you have done this, you are ready to unleash you new-found knowledge on unsuspecting opponents. In every game look hard at every potential L&D situation and see how many basic shapes you can reduce the shape to. Sometimes it is only one, but at other times there is more than one basic shape in the position and you have a choice as to which one to make. When you can do this and make that decision based on a global perspective, and do it more or less on sight, then you understand the position. Not before.