Hearthstone: For Beginners

The Meta

There is a few things to learn. Firstly you've done well to get to Rank 16 and that is about what you can expect without knowing every other class well so you can effectively play the meta-game which is; the game within the game or put more simply playing against what you think/know your opponent will play/do next.
The quests that Blizzard give you daily are a way to learn every other class, and you should try seriously to do well with every class to learn their intricacies.

Control vs Face

There is a fine line to learn between when you will draw the best value from either controlling the board and clearing minions or doing face damage to your opponent to apply pressure. Obviously this varies from class to class and even deck to deck but it is still a skill that higher ranked players have learned. The best way to learn this is to watch legendary ranked players either on twitch or youtube, watch ESL finals series because you know those matches are being taken seriously. Applying face pressure can do all sorts of things to your opponent's game plan and will often force them into a defensive role – BUT if done incorrectly you are handing your opponent board control and they will likely overpower you in the end.

Value from cards/minions

Learning to extract maximum value from minions can be tricker than most people think. For example if your opponent has a 1/1 minion on the board and you have a 1/1 and a 2/2 you should clear his 1/1 with your 2/2 and face with your 1/1. Even though you're doing less overall face damage you are going into his turn with 2 minions on the board instead of 1. Sometimes it seems counter-intuitive and again the best way to learn this is to watch better players play.

Patience

Another thing that can seem counter-intuitve is to be patient. Sometimes the best play is to pass and play nothing. Try to take your time and calculate value, if you have a card that will work better in a combo then just wait. Don't play stuff just for the sake of burning mana.

Enjoyment

This seems like it's not required to be good but I think it is. You have to remember that at the end of the day not only is Hearthstone a game, it's a game of skill and luck. You should be prepared to lose 25-45% of your games and not get angry. If you are getting angry, walk away.

Additionally to enjoyment – if you're scared to lose you won't progress, protecting your current rank will make you play defensive and kill any enjoyment. The best way to progress is to play LOTS of games, so don't worry too much about your current rank and just aim for a better than 50% win rate. The wins will come and so will the losses.