The most important thing to remember is to protect your Command Center at all costs. The best way to do this is to put it in the center of the map, surrounded by other buildings and with traps, turrets, and towers arranged to wipe out the enemy while they're attacking the other complexes.
Walls are tough to penetrate. One of the simplest and effective base designs is to surround everything important with walls.
It's easy to forget how valuable time can be. You can pay diamonds to save time, but in some cases, it's better to hold onto them and let things happen in real time. Training units and making low-level upgrades don't take too long.
Always be building and upgrading resource storage when possible. Resources are necessary for most upgrades, and you can never use more resources than your capacity allows. Not even using diamonds.