Zerg defenses are simple and tough to break. The main defense is Spore Colonies around the perimiter. Then Sunken Colonies by the ground enterances. Then have Zerglings and Hydralisks burrowed around the Colonies and all around.
The best attack is with the Hydralisks and Zerglings. First, swarm the enemy defense and destroy as many units and buildings as possible. Next, you have at least 24 Hydralisks attack. While they are attacking, keep track of their hit points so when one is about to die, you can make them burrow so they can regenerate. After they regenerate, attack and keep burrowing when one is about to die. (remember to always have reinforcements on standby and, this strategy doesn't work when you're attacking other Zerg.)
The Zerg aren't good at air attack but they have a few tricks up their sleeves. The best air attack uses both Mutalisk and Guardian. First, get a lot of Mutalisks and Guardians and have them go towards the enemy base. Next, have your Mutalisks mainly attack air forces while your Guardians attack the buildings and ground units. (this attack shouldn't be used a lot. You could also use ground units in the attack but, it's all up to you.)
The Zerg are the best at brute force. First, get about 10-12 Ultralisks and attack the enemy base. While they're doing that, have lots of Mutalisks attack from the side. Then, you have Zerglings and Hydralisks attack from anywhere. (you could use the burrow strategy for the Zerglings and Hydralisks.)
The best attack with Ultralisks is to first, have lots of Zerglings attacking the outside of the enemy base. Next, have the Ultralisks attack. Also, have Hydralisks behind them in case they have some flying units.
When or if you have an infested command center, use the infested Terrans a lot because they are very usefull when you need to weaken their forces.
When you have a Queen, use her to parasite Shuttles, Dropships, or Overlords so if they are transporting units, you will know where they are dropped off. Also parasite any units in the defense perimiter so you will know what kind of things they have.
When Zerg are attacking Terrans, use the burrow strategy. When fighting other Zerg, use brute force. When fighting Protoss, use airial attack.