The best way to improve at Starcraft 2 is to play a lot. It sounds silly, but it’s simply true. When I started playing, I was originally placed in gold league and stayed there for a full three months. Then, slowly but surely, I rose up until I was in the top 50 Grandmasters in America.
Obviously, not everyone can become a Grandmaster (it requires, amongst other things, exceptional reflexes, reaction time and coordination), but I firmly believe that, with practice, everyone can become a master at Starcraft 2.
The first thing to work on is understand the game mechanics, namely: armor vs non-armored, range, attack speed, damage reduction, hidden bonuses, splash damage, etc. For instance, one thing that makes the Terran siege tanks so powerful is the fact that they might hit not just one unit, but up to 8. Obviously, the 70 damage they can quickly become 300-400, making them one of the highest-damage units in the game.
Every unit has its particularities and becoming intrinsically familiar with them will greatly improve your play. Any Protoss player, for instance, knows how to individually blink their stalkers to save them as they are about to die. Likewise, a Zerg player knows not to group their mutalisks during a raid if the enemy has air splash damage, such as a Thor.
The second thing to improve on is your knowledge of group battles. Almost all Starcraft 2 games are decided by one large confrontation, where the loser will be left on the defensive, rolling back, while the victor will keep pushing and destroying the economy and production capacities of the loser. It is better, in my opinion, to retreat from a battle that is clearly lost rather than lose every single one of your units in a lost defense. There are such things in Starcraft 2 as pyrrhic victory, where you somehow manage to hold a magnificent defense, but lose so much time and resources in the process that your other bases are left defenseless.
Another key trick to improve at Starcraft 2 is to utterly master the art of macroing, i.e. producing units, mining bases and, most of all, expanding. If you watch professional games, you’ll notice all of them expand very quickly, sometimes dangerously fast. While risky, an early expansion can bring him double the amount of minerals and gas you’d grab on one base, giving you a decisive advantage in the mid-game.