A few of these have been mentioned already, but a few tips off the top of my head as a fellow random player...
1) As Protoss and Terran, you should never stop building Probes or SCV's. Try to always have one in production.
2) As Protoss and Terran, don't overqueue units. For example, you should never have like 3 Marauders queued at a single Barracks. If you have that much money, you should consider producing an additional Barracks instead.
3) As Zerg, you need to scout your opponent as much as possibly and play very reactively. How do you know when it's safe to make Drones, or when you should be making a bunch of units to defend against an incoming attack? Should you stay Tier 1 and tower up a bit to survive the 4gate push, or should you get to Tier 2 and get Hydras? This is the sort of decisions you need to make, and you can't make these decisions without knowing what your opponent is doing.
4) As Terran and Protoss, the above applies, but you don't need to play so reactively. You can follow some general builds and unit compositions and still be in a fairly safe position.
5) You always hear this cliche, but it's famous for a reason: the best defense is a good offense. Towers can only accomplish so much. Towers are favourable in three common scenarios.
Scenario A - You're Zerg, and you can't possibly produce enough units to defend an incoming attack due to larvae restrictions.
Scenario B - Your army is very immobile, and thus you can't be expected to defend your base whilst moving out and attacking. (ie. When playing against Mutalisks or Banshees)
Scenario C - You need detection to protect your mineral line. (ie. DT's, Banshees, etc)
6) Knowing when and how to expand with each race comes with experience, I can't offer much more in that regard. However, if you've got more than 30 workers in your main base, it's definitely time to expand and shift half of them over to your new mineral line so you can capitalise on the high worker count. Ultimately it all comes down to what map you're on, where your opponent is located, what strategy he's using and whether or not you can afford to safely secure your expansion whilst having enough units to stay alive. This is especially critical for Protoss, since as a Terran or Zerg player, you're still yielding the benefit of additional MULE's/Larvae from a 2nd Hatchery/Command Center that isn't harvesting minerals.
7) Watch replays, learn build orders. But don't strictly rely on them. Just use them as a foundation for understanding the dynamics of each matchup. From here, you can twist the builds and add your own styles to try out new strategies. But for the time being, I'd recommend sticking to a single race and learning 1 build for each matchup before moving on to a new race.
8) Understanding unit counters is pretty important, and as a Random player, you'll be a lot more switched on to unit costs and composition requirements than most people who play a single race. For example knowing how many of X are required to beat Y, or being able to evaluate your opponents army value at a glance, and knowing how much you need to invest to match it. Hotkeys are also important. Sure it doesn't seem like a huge advantage if you know that the hotkeys for Zergling Speed, Baneling Speed, Stim, Marauder Shells, Combat Shields and Pre-Igniter are M, C, T, G, C, and I, but over the course of an entire game, those tiny time-savers can really add up.
9) Psychology is very important. You can trick (or force) your opponent into making a certain unit type by controlling the information you give them. Some examples would include building a Roach Warren or Baneling nest in plain sight, whilst hiding a Spire elsewhere. If a Terran scans your base and sees either of those structures, they won't favour Marines or Thors in their unit composition, which allows you to capitalise with Mutalisks.
10) Multitasking. Being able to micro a small force (or several small forces) at once whilst expanding, teching, producing units or queueing workers is one of the most important skills of the game. It's all well and good if you micro like a king and manage to take down 5 Stalkers with your 3 Marauders and 4 Marines, but if you've got 1500 minerals and you're supply capped after the fight is over, your opponent is going to recover and beat you with a counter-attack.
Hope you find some of this valuable.
Posted on Tuesday, 28th September 2010