A few tips from me.
One, know what the races can do. No, I am not talking about some minor differences in size between the Ultralist and a Thor, but just the general powers that the entire race has. For example, don't try to attack a Terran's base with ground to ground units only, since they can lift the command center and all the production facilities away and land some where else. Knowing the basic powers, and knowing when they will use it will get you wins.
Two, tricking your opponnet into investing in counters of units, say making a Protoss think your going Mech by letting them seeing factories you built in your base while actually going MMM in a hidden base somewhere, they go an immortal build. Tricking you enemy with your build will often leave your opponet unable to deal with what your actual army is.
Three, don't just go one kind of units, have some diversity in your army. If you go only one unit,or one kind of unit, your opponet will steam roll you with hard counters like nothing you will see before. Your going a Rouch build? Throw in some Mutalists to deal with air units, or going a templar build? Make some Immortals to take most of the hard damage. Having multiple unit types will make your army less of a hard counter to anything, but much harder to beat.
Four, look around the map, espically as zerg. With overlords, one doesn't have any excuse to not know about the more important expansions and knowing what is happening at the major choke points. You may lose an Overlord when the enemies army comes by, but you know now that an attack is coming, they are taking another base, etc. you can act accordingly. If your not Zerg, have flying units do the occiassonal lap around the entire map.
Five, get bases besides your natrual. Exapanding is key, and if your out expanded, you have lost the match since your enemy can out mine, and just fling units at you until your dead. Hiding expansions can make enemies either unprepared or paranoid, giving you an upper hand.
Six, deny enemy bases when ever you can. Same reasons as above, but with a different twist. If you can prevent your opponet from getting bases while getting your own, most of the time you can win. Having Overlords dumping creep at possible bases means they can't build anything until the overlord is dead/gone, and the creep disappears, and I think it takes 30 second for the creep to go away. That is a long time to just sit on the minerals. Another strategy as Zerg is to get burrow as quickly as possible, and put one zerg at each base in the field. Newer players will think the game is bugged, and more experienced players will have to waste money/energy on observes/scans to just find the little critter and take him out.
Seven, in 2v2, know how you can help your teammate. If your Terran, know that SVC's can repair Protoss robots, while Medivacs can heal all Zerg units. If your zerg, don't put creep in their base unless you ally is also Zerg. If your Protoss, you can Crono boost allies production factories to have them make units faster. Go different tech types, one goes heavy on the infantry while the the other goes heavier mech or similar. Pull your own weight.
Edit: Eight, know hard counters. You don't need to know that if one ____ and one ____ that ____ will kill _____ slightly faster, but that Immortals do extra damage to armored, that Marines counter light air, that Collosus counter weak one tear units in mass, Void Rays counter big health units, etc. If you don't know basic counters, you will be steam rolled by those that do.
Edit 2: I have been informed that Choroboosting allies buildings has been removed form the Beta, so disregaurd that bit of advice.