I have never played any other RTS online due to a whole host of factors (never had fast internet as a kid, as a college student I couldn't afford to buy the games and didn't have the time in general.) I didn't even know that much about the Starcraft community when I started playing.
So here is a step-by-step guide of how I got into 4 different leagues in 4 months.
Step 1: Pre-Bronze: Before you start playing anybody online learn the hotkeys.
When you start playing in the bronze league you'll will either be playing people who have only point and click, or can barely use the hotkeys. You'll quickly rise through the ranks of the bronze league if you know how to use your hotkeys.
Step 2: Mid-Bronze to High Bronze: Learn a general build.
You'll have the edge if you can produce units faster and more efficiently than your opponent. This will also become the foundation of all your future play, so learn a macro-orientated build. This means that you want to be making an expansion in some part of your build.
Step 3: High-Bronze to Top Bronze: Know your units.
If you play zerg, terran or protoss you have to know which unit hard-counters and soft counters each unit, so if you see Marauders at your base, you want to be producing Lings, if you see Hydras at your base you want producing Collossi... etc.
Step 4: Getting into the Silver League: Unit compositions.
From this point on you will need to know that having a bit of every unit is more of a hindrance than it is a help.
-Terran, who have the most variety in units, are designed to be defensive power houses, so the most common unit composition is marine/tank, the counter to this from zerg is ling/bling/muta. Some other builds from terran, which are becoming very popular, are Mech builds (hellion/thor/viking) and the response to this from zerg is roach/infestor.
-Protoss on the other hand are a power-overwhelming race, when they get a 200/200 army, there is little any race can do to stop them. The most common unit-mix for Protoss in called the death-ball which is Zealots at the front to take damage, Stalkers/Sentries in the middle to wall off and defend your most valuable unit, the collossus, collossi in this mix deal huge amounts of damage. Zerg's response to this is roach/hydra/festor/corrupter.
-Zerg are, as outlined above, a responsive race, whatever your opponent builds you want to be considering a definitive counter to.
These compositions above are merely a handful of the possible compositions that are available in the game, consider exploring the many, many others, and never become too invested in your unit composition because the game is always changing and eventually your unit composition will become dated, and everyone will know how to beat it.
Step 5: Establishing yourself in the Silver League: Know your opponents builds and scout them.
This is where things get a bit more difficult. You may have only 50 games or so under your belt at this stage, but you should be able to start predicting what your opponent will be doing, even if it is the most basic sort of predictions.
-He has got gas early, he must be getting tech.
-He has no gas he might be expanding or he might be cheesing me. Is he building lots of unit producing structures? No. Then he is expanding. Then I should expand too.
If he has a lot of unit producing building then he is cheesing.
-He has got both gas geysers early. He is going heavy tech possibly air units (Banshees, Void Rays etc.) get some static defence.
Step 6: Low-Silver to Mid Silver: Learn more builds.
The overall build you learnt in the bronze (whether it be 1 Rax FE, 15 Hatch, or Forge Fast Expand) will start to become too rigid for all the varieties of play you will start to encounter, so now you'll need to learn race specific builds. Spend sometime learning a new macro orientated build, (Hellion Expand, 2 Rax Expand, 14 Pool - 18 Hatch, 3 Gate Expand Etc.)
Step 7: Mid-Silver to Top 8 Silver: MACRO, MACRO, MACRO.
If you can out Macro your opponent; produce an army faster than he can, you should win nearly every match, no matter how you control your units.
Step 8: Cementing yourself at the top of the Silver League: Learn how to beat the 4 gate.
This may be a slight deviation from all my other steps, but this one is quite essential. From Mid-Silver to Low-Gold, 90% of all Protoss players will 4-Gate you, if you can beat the 4-Gate you will win 90% of your games against Protoss.
Step 9: Getting into the Gold League: Refine your scouting.
You need to be scouting almost constantly from this point on.
You will need to know when your opponent will be pushing out, or what units he is constructing, or what tech path he is going down. Observers, Scans and Overlord/Overseers, should become an integral part of your play-style. You should be now playing so you won't lose.
The two most important times to be scouting with your 9 worker (to know where your opponent is, to make sure you get a unit into his base before he walls off, and to see if he is cheesing you) and at the 6 minute mark (at this point your opponent will be choosing his tech route and be moving into the mid-game.)
Step 10: Establishing yourself in the Gold League: Base Management.
You do not want your opponent out-producing you/getting a better economy than you. So you want to make sure he does not get a third base up and running. And you want to be constantly probing and prodding the place where he'd be most likely be getting his third base, and occasionally checking the other places where he could be establishing a base. You also want to be expanding yourself, so move your army into a position where you can secure a third.
RACE SPECIFICS (Zerg): As Zerg you want to be at least one base ahead of your opponent at all time, your units are weaker than the Terran and Protoss Units, so you want the economy and the Hatches to be able to produce as many units as possible at the drop of a hat.
For other races you want to be harassing the bases of the zerg as much as possible. And keep this thought in mind: "You can never out-macro a Zerg."
Step 11: Mid to High Gold: Everything has to be crisp. You want to be refining your mechanics at this point. If you are not using your grouping keys, start using them. You putting down your expansion at 450, make sure next time you are putting down exactly at 400. These minor, minor things will eventually add up and you'll find yourself losing to a lot of timing attacks, and early pressure.
Step 12a: Getting into Platinum (Part 1): Know your maps. Every map in the game has weaknesses and strengths for each race. For zerg you want to be engaging your opponent in open areas. For terran you want to be engaging your opponent at a choke so you can draw them into areas where you can out range him. And Protoss wants to be engaging at a place where he can easily retreat because your army is so strong at 200/200 you want to save as many units as possible for the mid-late game.
Step 12b: Getting into Platinum (Part 2) Positioning.
This is pretty much an expansion on the last point because when you know the map, you will know where to position your army properly, now comes the how.
For Range units you will want them spread out in a wide concave so they can all deal damage at the same time.
Also remember stronger/cheaper units at the front, and the more fragile more damaging units at the back. For example: Roach/Hydra in ZvZ, you need to make sure the roaches are at the front, they have a much shorter range, but are much harder units to destroy, the Hydra however deal way more damage and out-range the roaches, but die quicker.
Tools that will help you improve:
-Your own replays. Your own replays are an invaluable source of information, it always has the answer to the one thing you'll also want to know; "Why did I lose that Match-up?"
-Day[9]. Day[9] is possibly one of the greatest the strategists in SC2 at the moment, he has a very natural and deep understanding of the game, and he covers both advance and beginner methods in his videos.
-Pro-replays. These people play starcraft 2 at the highest possible level, they know every little possible detail about the game, and by watching them you will understand how they approach match-ups, and they scout, and what unit compositions they use.
-Communities. Communities such as Teamliquid offer and invaluable service to all players involved. If you can't see why you lost a game, than maybe a better player will know what you did wrong, never feel ashamed to come on to these websites and ask for help, because we all started off in the bronze league. I also know that I don't spend a contributing to Teamliquid, but that's because I spend a lot of time on the Irish SC2 website (and yes I'm irish) boards.ie
Advice:
-Forget about cheese. If you lose to cheese don't worry about it that player will never become a good player, they may win a few matches, but eventually they will meet players who know how to beat them, and they will never win again, and stay indefinitely in the league their in.
-Losing streaks happen to us all. If you go on to SC2 ranks and look at my profile you'll see huge dips, at one stage I lost 9 games in a row and almost got demoted back into bronze. These things happen, it just means that you are not thinking straight, and keep on making the same mistakes you use to make. Just take a break from the game. Maybe 1-2 days, when you come back to the game, all the fundamentals you have learnt will return and you'll quickly get back into the swing of things.
-Never be afraid of the ladder. A lot of players say they are "afraid to return to the ladder" after a long hiatus, the ladder is not that daunting, you are put into a division with players that have just as much ability to play the game as you, and if you lose, you lose, the game will re-calibrate itself and you will eventually start to play people of equal skill.
Finally, have fun, because it is a game after all, and a great game at that.