Q:

How do I build and fight simultaneously?

I feel like my main deficiency is that I have a hard time with the multitasking required.  Specifically, when I have troops in the field, especially more than one group of units, I tend to not keep up with building (structures and units) and my resources just sit there, wasted.
What strategies can I use to keep up with building structures and units while I'm coordinating my troops across the map?

A:

StarCraft is partially a game of processing information. Multitasking is one of the main skills you improve while playing.
First, you need to use hotkeys. Use them to quickly get information on production status and jump to different groups.
With SC2, hotkeys can bind to multiple buildings or groups and you can use the Tab key to tab between them. Personally, for Terran, 1 is for command centers, 2 is used for my initial initial scouting SCV and then for general unit usage, 3 is always barracks, 4 is always starports and factories. 5 through 8 become groups of units in the mid- and late-game.
The above scheme lets you tap 3 and 4 to see production status of the army. Do this and, if you don't see white dots underneath the green building icon in the bottom console, start building something. (What to build is another discussion.) Cycle between your hotkeys to move units and check on production status.
Don't forget that double-tapping hotkeys takes you to the group, Ctrl and a number assigns the group, and Shift and a number adds units or buildings to the group.
Next, you really, really need to pay attention to audio cues in the game. Make sure to turn the music off so you can hear them more clearly. 
Finally, note that Space takes you to where the action is. Did you year "Our units are under attack?" Hit space, and you'll be taken to the action. Or maybe you'll remember which hotkey you assigned that group and you can double-tap it.
Hope that helps :)

A:

There isn't a good answer for this but I'll give you some of what I've found helps

Don't focus on your army so much, when you send it out stay focused on your base
When you're just about to make a push is a good time to expand (your opponent will be pushed back)
While you're in the middle of a battle build a couple workers.  New units usually won't get there in time (or you'll be capped on unit production), so its a good time to add in workers to rebuild after an assault (or defense).
Hot key your buildings, with Multiple Building Selection its really easy to have your production running from a distance
Make your pushes right after upgrades finish
Always set your rally points, even if its just to the nearest choke.

I hope these help.

A:

In addition to most everything a paid nerd said, I would add a couple things.
Playing StarCraft well is similar to driving a car well. You need to pay attention and check your mirrors a lot to ensure you're fully aware of everything that's going on. With practice, you can get into a nice rhythm of checking on the fight, checking your building production, glancing at your base, and throwing up new buildings.
Specific things to watch out for:

Are your workers idle? There is an icon in the bottom left that pops up whenever that happens. To help avoid them going idle, use Shift to queue up actions such as "Build a Factory, then go back to the minerals."
Are your buildings building units?
Do you have too many resources in the bank? If you start to get high, you likely need to produce more, which may mean more production buildings.
Are you running low on supply?
Did you accidentally leave a bunch of units sitting next to your buildings?

