Unlike the 1000s of Starcraft pages out there, I'll assume that you've played Zerg before and know the units. I won't have any pictures or information on the costs of units and buildings here. If you're unfamiliar with Zerg units, then I suggest that you take a brief look at your Starcraft manuel.

Drone - These are the Zerg's workers. Like always, you'll need tons of them. If you researched burrowing at your hatchery, then you should utilize it with your drones. So if you're drones are being attacked, burrow them until help arrives!

Overlord - Although they cannot do any damage, these can be very useful. Many beginners only use them to house a huge army. That's the most important function of overlords, but they can also be used as transports and scouts. Get all of the overlord upgrades available when upgraded to lair. If you suspect that your enemy's cloaked units are responsible for the mysterious deaths of your units, then bring along an overlord to spot them!

Zergling - Zerglings are your first line of attack/defense. You get 2 Zerglings from one egg so that can be a real bargain. I think two Zerglings only use up one unit "slot" so you won't need too many overlords to support a large army of Zerglings. If you rush your enemy with a large enough army of Zerglings with a speed upgrade early on, then you've probably already won. All you have to do is take out your enemy's buildings. Although Zerglings cannot attack air units, the enemy probably cannot build up a large enough air army to destroy your Zerglings quickly. Supported with Hydralisks, these guys can penetrate any early defense. Later on, you'll need to upgrade your Zerglings or they'll be ineffective.

Strong Against : Any early units if the zerglings vastly outnumber the enemy's units.
Weak Against : Air units, Archons, siege tanks (unless outnumbered greatly), and other advanced units.

Hydralisk - Hydralisks aren't very strong but they're very versatile. If you plan on building an army with mostly hydralisks, then the hydralisk upgrades in their den are a must. Their advantage is their cheap cost combined with their usefulness. However, many things can happen if you mindlessly build enormous armies of hydralisks with all of your available resources. You'll probably forget overlords and you'll have to go back and build those guys too. Another possiblity is hitting the unit limit. When this happens, you'll know it's time to upgrade more and attack. If your opponent discovers that you're going hydralisks only, he can build templars, tanks, defliers, etc. which are good at taking out hydralisks.

Strong Against : Wraiths (unless cloaked), scouts, mutalisks, marines, firebats.
Weak Against : Siege tanks, carriers, battle cruisers, guardians, ultralisks.

Mutalisk - These are the first fliers the Zerg can make. The one thing I don't like about mutalisks is that they cost a fair amount of gas and several dragoons/marines can destroy a small army of mutalisks. Build them if you're enemy cannot fight off air attacks or if you have a huge pile-up of vespine gas. It may not be that bad if you attack with Mutalisks early on repeatedly in large groups. This strategy is often used by many good Zerg players on Bnet.

Strong Against : Ground units that only wish they can hit air units; Bunkered marines, photon cannons, missile turrets, spore colonies.
Weak Against : Goliaiths, Archons, Templers (PSI Storm), defliers, and other advanced units.

Scourge - Scourges do 110 damage on impact but they also die themselves. One egg can hatch to 2 Scourges making it 50 net resources per Scourge. Taking out enemy carriers, guardians, arbiters, etc. with Scourges isn't a bad idea. Enemy overlords are an easy target for Scourges but you're only breaking even resource-wise if you do so. However, it's a real pain for your enemy if you take out all of his overlords before launching a devastating attack that destroys all or most of his workers. He cannot rebuild his workers without rebuilding his overlords 1st!!!

Strong Against : All air units.
Weak Against : Ground units and "towers" that can attack air.

Queen - Queens can cast three different spells : Parasite, Broodings, and Ensnare. I find that Parasite and Broodings are the most effective although occasionally Ensnare does have its uses. Parasite just simply helps you with your scouting since you can see the area around the affected enemy unit. Broodings destroys a unit and turns it into two broodlings. It's very effective against enemy tanks and Archons. The broodlings aren't really strong and you shouldn't count on them to destroy anything except for workers. Cast it on some of your enemy's workers and have the broodlings finish off the remaining workers. If you want more broodlings but there are no enemy units to cast it on, then cast it on the critters or even your own broodlings.

Ultralisk - Other than having a great deal of hitpoints, Ultralisks don't have anything special. They can do a lot of damage but they don't attack rapidly.

Strong Against : Marines, Dragoons, Firebats, Zealots, photon cannons.
Weak Against : Air units and Archons.

Deflier - I find that Defliers are valueable if they have Plague and Burrowing. Cast Plague on some enemy units/building and immediately burrow. Then wait until the Deflier has enough energy again and cast Plague again! Multiple Defliers burrowed near the enemy's town can really annoy your opponent, and if you attack the affected units/buildings, they'll be destroyed easily.

Guardian - Sadly, these fliers cannot attack other fliers. Useful only if your opponent has no air force and minimal air defenses. Making these guys can cost a great deal of time and resources. I consider these guys as the Zerg's wildcards since it's not really easy to use them to their full potential.

Strong Against : Missile Turrets, Bunkers, Photon Cannons, Spore Colonies, Marines, and land units that can't attack air.
Weak Against : All other air units and Archons.

Infested Terran - Wow!! They do 500 points of damage when they explode!! They remind me of the Sappers in War2. However, you MUST severely damage a Terran Command Center and infest it with a queen to make these guys. (Not to mention that you have to also defend the Infested Command Center.) Be careful that these guys don't explode near your friendly units when taking out buildings or you're friendly units will go bye-bye along with the building.