While becoming a great poker player requires a combination of a number of skills, there are two that a player must absolutely possess if he is to have any chance of succeeding at the game.
These are Mathematics and Self Control. For making informed and intelligent decisions and judgments while playing a game of poker, you need to know or need to have a very good idea of probabilities. You need to be able to mentally calculate these numbers. You need to be able to calculate the chance for the various possible ways in which you can complete a hand. You then of course have to take a decision on the basis of your risk capacity as to whether you are going to fold or go for it. But without this information, you are basically playing the slots.
The second most important skill is self control or discipline. You need to know exactly when to fold or when to hold. In gambling of any kind, there is a tendency for players to keep going after money lost. In poker, you need to know whether you are going to come out a winner at the end of a game, and based on the calculations that you have done you should be able to reasonably guess that. Once you have assessed your hand and your chances, you need to be very disciplined in whether you are going to continue playing or simply fold. The money that is in the pot is gone. Make your decisions based on the current bet. Evaluate your odds and adjust your self control to this important fact. Do not chase money because you have put money into the pot previously.
Both of these are the most useful and desired characteristics that a poker player needs. These take precedence over traditional poker stereotypes and having a good poker face. While psychology is very important, it will not mean anything if you do not have the above two qualities. You may have the best poker face in the world, but if you do not know what your chances are you yourself are basically playing in the dark, and hoping to use only psych to get at the competition.
It is very critical that self control and probability guide your knowledge of various paths that your hand can take. It should let you make some very good risk vs reward bets which is what is needed to understand the poker sill levels.