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 :)