It is just a matter of practice. I recommend watching Day9's "Newbie Tuesday" series and commented pro matches, he has a very handy video on basics here:
https://www.youtube.com/watch?v=RUohpQKVf_A
For macro, play a lot of Monobattle arcade maps, it is easier to macro there than in a ladder game, not so much pressure since you are playing in a team and without any ranks, and it is just more fun in some sense. That's how I went from clunky 20 FPS to over 120 FPS consistently when I was starting up. Also, you get to learn each unit's strengths and weaknesses, since you are only allowed to build one unit the whole game.
For micro, all kinds of "Micro Tournament" maps help tremendously. Just pick one map and play it a lot, and soon you will start picking up things that work and automatizing your actions without you consciously thinking on them.
It took me, I think, about a month of consistent (3-4 hours a day) play to get from "aaaaaarghhh, I can't do everything at once!" to a comfortable multitasking. Then it took another month or so to become good at micro - I played almost solely Micro Tournament kind of maps and got really good at it eventually. So, yes, it takes some time, but after you're done with it, you can focus on the actual strategy, rather than paying most of your attention to trivial tasks. It becomes so automatized at some point that you just forget you are playing with a keyboard and mouse, you just kind of think and react without any conscious effort.
P.S. Minesweeper helps a lot with mouse precision as well.