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Honestly, it's just an experience thing If you're receptive and honest you'll pick up things very quickly. Game awareness only comes with experience, but there are a few simpler concepts to be aware of.

! Don't tilt- Magic is a paper game and often you can "BS" your way through a game if you keep your opponent on their toe. Many games dissolve into formality and early submissions occur. Many players get the "it wouldn't have mattered" attitude and blame the variance of the game for their defeat instead of simply accepting the gamestate at hand and trying to move forward in the best way.

! Know when to step away from some sweet tech. There are lots of cool and capable cards in Magic, but when they are playing suboptimally, you need to cut them.

! Look for subgames to discover what is important. Often your card selection is done with a particular subgame in mind, be it playing and attacking with creatures for 20 damage, or plowing the field and pushing your opponent into a crumple-state. Magic is made up of subgames wherein what matters changes, the capacity to shift your priorities will allow you to overcome obstacles.

! Don't be afraid to admit when you are wrong and learn rules- It's a complex game.

! Learn how and when to play passively. Often it's better to just not cast a spell even when you have the capability to do so, or to take damage from a creature you will probably remove later anyways (to bait more board presence for a wipe.) Learning when not to act is absolutely integral in knowing when to act. If this confuses you, try cards that behave similarly to Impulse , some cards are designed to support passive play and through experience with them, you learn how to avoid knee-jerk reaction.

! Own your role, but don't be owned by it. Many players (self included) like a particular "style" of deck that is designed to play a specific role (aggro vs. control usually)- but learning multiple roles is important to growing as a competitive player. Often, players who are finally comfortable playing the passive game begin to look down upon "aggro"  and "midrange" decks as being "less skilled" than durdly do-nothing control decks. The only granule of truth to this is that super aggressive decks are slightly more forgiving, but the level of awareness and skill IS important to playing all roles. Don't let comfort with a role become a crutch.

! Know when to take some time away from the game. Ruts happen. And distance is often the best way to return to the game and have fun.

I would like to chime in. Practice your deck as often as possible, against as many decks as possible. One of your best and only guarantees for advantage is knowing exactly what you could draw. How many clifftop retreats do you run, how many have you drawn? What cards haven't you drawn? Be as familiar with your own deck as possible, and know its weaknesses. Then, design your sideboard to deal with these weaknesses. For example, I have a very good match-up against other aggro decks. I went to Star City Open a couple weeks ago, and my sideboard was built 10/15 cards for control games. Round 1 I lost because I was so nervous. My opponent saw that and leaned against it, and made me misplay. Afterward, I was kicking myself because I had a good match up against his Jund Midrange build. Later, I was 5-2-1, and I'm going into the last round. My opponent is playing Jund Midrange again, but now I'm much more relaxed and comfortable, because I've been doing well, had lots of 2-0 wins. I'm not nervous. I play my deck right, and I win my games quickly. My opponent shakes my hand.

I also like to use a card or two that aren't seen even marginally in the meta. I run human aggro, and nobody expects Rally the Peasants. I have three red sources in my deck, and I had some opponents asking all games one and two, "What is the red for?" Then game three, I have Rally in my hand, six lands open, including a red source. I attack with three 1/1 tokens, a 2/2 soulbonded Silverblade and the 4/4 Champion of the Parish he's soulbonded to. He chumps the Champion, being at 13, and willing to take 7. I cast and then flashback Rally before damage, turning seven into 27. He said, "Oh, that's what the red is for." The advantage of using cards your opponent doesn't expect can be huge.

Muligan often.  If you aren't mulliganing at least once a match, you're most likely not doing it enough.

Shuffle thoroughly.

Don't block.  Crack back. 

Know the rules.  It sounds obvious, but learn them as well as you can.  Aside from experience, nothing helps you play better than really understanding how everything works. 

In particular, learn how the stack (and priority) works and learn the phases of the turn, especially combat.  Knowing how to use those to your advantage give you the most opportunity to play all kinds of tricks.