First of all, the fact that you're actually willing to improve and practice tells me you'll probably get good quite quickly. This mindset alone is one of the most important factors when it comes to who gets better and who gets stuck in Noobville.
I don't think there is a "best and fastest way to improve" that works for everyone though. We are different and I believe at the end of the day everyone has to put in a lot of effort to actually get good. I don't think there is a magic formula that will work as a quick fix. That being said there is a lot we can all do to optimize our training and more efficiently use our time.
Things you can do on your own:
1. Practise the build order
If your build order is bad you'll constantly find yourself in situations where your opponent has more stuff than you. If you have 6 swords and the opponent has 18 it's extremely difficult.
I recommend starting a game vs easy computer, play the opening, resign and look at how well you did, then repeat. Ideally you should start a new game every time since a big part of the opening is setting up your base with the map you got. For Mid SH I suggest playing until F11 3.
2. Read and watch guides, and watch others play (observing or youtube videos)
Even for expert players I recommend reading guides/watching lots of games by others, because it's very unlikely that you as a player know everything and you'll probably pick up something new. Also you could identify mistakes by others and learn from those as well.
3. Ask questions
Like you're doing now, ask a lot of questions. If a good player does something in a game and you don't understand why, don't hesitate to ask them (preferably after the game). Usually there is a good reason and most players are willing to explain and help new players when asked.
Things you can do in multiplayer games:
1. Play opponents that are better than you
Playing someone better is brutal since you'll end up losing a lot, but for most players I think it's probably the best use of their time. If you're making a mistake but you're playing someone terrible, you'll probably be able to get away with said mistake and win anyway. This way you may develop a lot of bad habits. On the other hand when you're playing someone better not only will you not be able to get away with those mistakes, but they will identify mistakes in your play that you didn't even know about.
2. Prioritize 1 vs 1 games over team games
You can learn a lot from team games, but there is undeniably more down time in them. Also everything is up to you in a 1 vs 1 game, you won't be able to rely on team mates to carry you. An extra plus is that there is usually less waiting between 1 vs 1 games than team games, so again this is more effective. Ideally you find someone to do a 1 on 1 sessions with, where you two basically play non stop for awhile.
3. Vary between 1v1, wing and pocket
Focusing on one of the three for a time is fine, but you should mix it up every now and then. Playing all roles will give you a better understanding of the game as a whole. As pocket having a good wing or a bad wing will have huge impact of your game, and you will learn what the wing can do to help you as a pocket. So next time you're wing you'll try to do those things. This also goes for playing very aggressive and playing very defensive, you should mix it up.
General Do's and Don'ts:
Do your best
If effective training is what you're after then slacking and fooling around is not what you're suppose to do. Set yourself objective goals for the session and aim to reach it.
Don't be too hard on yourself
Learning and improving at an RTS game is not easy. Some of the players you're up against has over 50 000 EE games under their belt. Patience.
Don't make up unnecessary obstacles for yourself
One very common thing people do is they make up rules in their own head about what you should and shouldn't do in a game. For example: "I don't like full wall, so I won't do it." If the goal is to become a better player then throw all those rules in the bin. If you're playing someone that have certain rules, make it clear they need to communicate that before the game starts. This way everyone is on the same page. I've no problem following rules like "no animal killing" or "no diffraction shield on nukes", but it needs to be made clear to everyone before game starts IMO.
The reason you shouldn't do this is you're basically putting yourself at a disadvantage. You want as many options available to you in every situation so you can make the absolute best decision. Sometimes the best decision is to make a wall around your base, if that's the case don't hesitate.
Do play/behave in a way that makes others want you in the next game
Hopefully self explanatory, but something we all (me included) have to remind ourselves off. In an online game, especially if there is competition involved, there will be shit talking and fooling around. Nobody expects everyone to behave like a saint 24/7, but we also expect you to not be an asshole 24/7. If you're not allowed to play online, you can't get better.
Well, this post got longer than I had anticipated. I guess I could write a book on the subject. I could go more in depth and answer more questions if you'd like, but I think this is plenty for now.