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 :)
At first, the credits available to you in the single player campaign is limited to that from missions alone. However, once you've fully maxed out either the zerg or protoss research trees, you gain the ability to trade any future research points into 10k worth of credits.
There have been mentions of a glitch with the way the game handles this: if you replay a mission you've already beaten and acquire protoss / zerg research points within that mission, it is possible to get the Moebius foundation to "purchase research samples" from you, even though you failed to increase your net points (you already got them once). In this way, you can accrue as many credits as you need, and can buy all the armory upgrades in a single playthrough.
Update: This method has since been patched.
As of now, the best way to earn the armory achievements is to play the campaign multiple times, selecting different upgrades on each playthrough, as achievements are shared across all campaigns.
Best Answer
Develop a mental checklist.
Day[9] has an excellent video focused on encouraging you to keep thinking about a small series of specific tasks or thoughts throughout the entirety of the game. When you start off, your mental checklist should probably be limited to about 4 main things:
Because of the way that the HUD is arranged, this means that ideally your eyes should constantly be darting back and forth between the top right and bottom left corners of the screen.
So to address your specific problem of being supply blocked consistently, you should create a mental trigger that associates a common task with checking your supply, so that every time you perform that task you don't even have to think before your eyes dart to the end of the screen. In this context, the action that makes the most sense to associate with being supply blocked is making a unit. In other words, everytime you make a unit, check your supply count.
It'll be difficult to get used to and you'll still slip up occasionally, but if you keep on trying to remember this, eventually you'll develop the habits necessary to keep on checking your supply count and thereby remembering to get that supply depot up on time.
Also keep in mind that as you expand and make more production facilities, your supply will go up faster, so while a single SCV producing depots will work for one base, eventually you'll need to keep two SCVs making depots in order to keep up with your supply as you expand.