The veterans should note that this will mostly be information for newer players, but it might be worth a read. You could always learn a thing or two.
If you haven't read the Zerg Scouting Compendium, I would recommend reading it. It's pretty good information, and very helpful for new Zerg players.
http://us.battle.net:80/sc2/en/forum/topic/248295026?page=1 - Scouting Compendium
In addition to that, Antpile wrote a GREAT guide on how to defend the Four-gate, which is Protoss's most common opener. Here's a link to that, I would also definitely recommend checking it out. Again, all the credit for that post goes to Antpile.
http://us.battle.net/sc2/en/forum/topic/248417801 - ZvP Four-gate guide
Disclaimer - Before I start this guide, I'm going to give everyone my personal opinion about the Zerg's standing right now in relation to the Protoss and Terran (Terran specifically). I do think that the Zerg could use a few minor tweaks, as we are lacking in certain areas. I won't elaborate on exactly what I think could be done, because that's not the point of this post, and I don't want a raging, pointless debate about balance going on while people are trying to ask questions. So, here's my official stance - while the Zerg could use a few minor changes, those don't become evident until you're at a very high level of play. For the intended audience of this post, that doesn't apply to you. So, let me say this. If you lose to Terran or Protoss, it was your fault. Accept that, move on. Watch the replay. I cannot stress this enough. Chances are, there's something you did (or failed to do) that caused you to lose the game. Find out what it was, and fix it next time you're in that situation. Don't bring your anger and frustration to the forums, because, to be honest, it makes you sound like a big baby whiner and nobody wants to hear it.
Now then, on to the main event.
For a newcomer to StarCraft 2, choosing the Zerg as your primary race is both a great decision and a bad one. Why? Well, the Zerg are unquestionably harder than Terran or Protoss when it comes to gameplay mechanics - macro and micro, mainly. However, in order to perform at all as a Zerg player, it demands a high level of skill, focus, and general knowledge of the game. Due to this, players that learn the game from the perspective of the Zerg are (in my opinion) eons ahead in skill development than someone who starts with Protoss or Terran. Like MacabreDerek says in his "Tale of Two Mentalities", "It's a tale of two mentalities, one focused on winning the game because of catching an opponent off-guard, and the one who is willing to learn the game and grow as a player." This is SO true for Zerg players, because I can personally guarantee that before you start to win games as Zerg, you're going to have to learn a hell of a lot about this game and you're going to have to be dedicated. However, if you pull through the ugly patch of your first fifty or so games, it pays off tenfold.
Okay. Now we're actually on to the main event.
We'll start at the start. With build orders.
Since the Zerg only have one production building (the Hatchery), their build orders tend to be a lot more vague than Protoss or Terran build orders. Since both Drones and army units are built from the same building, the actual build order you're using pretty much doesn't matter by the time you hit around 20 supply, because that's the point where you have to start adopting to your opponent's build. However, that first 20 supply is pretty crucial, so we'll go over the standard ones.
Every build order in the game is focused on one of two things - rushing, or setting up a strong economy and teching up. Zerg have some very strong options for both, so we'll go over them. Note that when I write build orders, I'll say things like "9 Overlord, 10 Pool". The numbers represent your supply level - at the beginning of the game, basically, this is your number of Drones.