How To Study
To start off, I'd like everyone to know that this is completely an opinion piece. Even at the very top levels of chess, superGM's will answer this question differently. However, here, I'd like to share my opinion on the most effective way to study the game of chess.
The answer to this question isn't so simple. The fact of the matter is that what you should study depends largely on your skill level. Total beginners should focus on learning the rules. Once that is 'studied' simply playing the game with opponents stronger than yourself will teach you the basics of strategy. For the purpose of this blog, lets say you are rated somewhere between 1500 and 1700 (An average tournament player).
At this level, your main form of 'study' should really come from playing games. However at this level a basic knowledge of endgames and openings are key.
A good study aid (at all levels) is the Chess.com Tactics Trainer. Use it! Use it often! Even the very strongest players use tactics training programs to keep their ability sharp. You would not be wrong to build your study program primarily around this program.
If you haven't read it already, I personally suggest How To Reassess Your Chess by Jeremy Silman (an excellent writer, his chess mentor courses are fantastic as well). That book gave me what I needed to know to break out of the 1700's.
Silman's Complete Endgame Course is another 'must have'. In it's pages are all the basic endgames worth knowing. Even if it is very simplistic at first, study it from the beginning, all the way up to your rating class (the book is divided into sections based on the readers rating) and one class further. As usual, Silman makes difficult concepts seem rather simple. Take your time going through this book though, because you may not have many chances to absorb the concepts through practice.
Finally, study master games! There are several approaches to doing this but I suggest going into a database, searching for a particular master who specialized in the line you want to play (if you can't find a superGM who uses it regularly it's not worth playing), and printing the PGN's of the games he won (and possibly drawn if losing your mind is the goal) and playing through the games over a board. I suggest doing it over a board for a couple reasons. One, it will help you remember the theory and key ideas over the board. And two, it will stop you from moving through the game too quickly. At the same time, I do not suggest playing through the games painstakingly slowly. As you go over dozens (potentially hundreds) of games played in the particular opening you want to know, you'll quickly pick up when and where certain key ideas should be used. Memorizing the games is not necessary.
Sound like a lot? In a way it is. The nice thing, though, is that it is cheap ($30 for a chess.com membership, another 30x2 for Silman's books = $90), and you can do it at your own pace. The more you study, the faster you'll improve, but it's ultimately up to your schedule.
Tactics, Openings, and Endgames! In short - EVERYTHING
Just my two cents... :)