TL;DR It's time to revive the blog! Only this time, I'm stylin' like Gentleman Cho'gath. That's right; WoW is old news, League is where it's at!
In all seriousness, I've actually been on League since early July 2010, so I've been around a while. I've just had an itch to blog recently, and to start becoming an active member of the community. While working on a guide for my current favorite champion, Pantheon, I've decided to also start up this blog for various purposes. Teaching strategy and giving tips, talking about various champions, things of that nature.
To start off, I've decided to discuss general team comp forming.
Something I've noticed is that very, VERY few people know how to 'round out' a team comp with their champion picks. It's difficult to do so as first or second picks, but 3-5 should be the rounding picks, and should be based not only on your lane matchup, but the enemy team as a whole.
For example: I have Cassiopeia and Vayne on my team as picks one and two. Between those two alone, the team has exceptionally high damage output and potent counter-initiation, but is lacking poke, bulk, and an initiation.
Additionally, you see the enemy team has Irelia in top lane, a Warwick in the jungle, and a Ryze. The enemy team has exceptionally strong initiation and lockdown power to be applied to both carries, while also having a LOT of prolonged teamfight power. The longer a fight lasts, the worse off you're going to be.
Therefor, you need the following: A strong burst initiation, strong ganking power from your jungler, and a lot of slowing/peeling power. To achieve all of this, you're going to want a tanky, CC heavy support such as Blitz, Alistar, or Leona for breaking WW's ult. Your jungler can be a tank-oriented Lee Sin, Maokai, or Jarvan, or Malphite specifically built for strong ganks, peeling Irelia off of Vayne/Cass, and bringing initiation power. Finally, you're going to need damage in your top lane, and a lot of it, so that you can end the fight before the sustain of the enemy team can drag the teamfight out. You want them to be relatively durable though, so that they can bring their damage without being a primary target for teamfights. Olaf, Vladimir, Fiora, and Jax all do this very well. Another route is to choose somebody who has slightly less killing power, but bring a heavy dose of CC. Champions that fulfill this well are Wukong, Kennen, and Hecarim.
This gives you a team with heavy initiation power, strong burst and killing power, peeling and counter-initiation, and a good dose of CC. A well rounded team such as this is incredibly hard to beat, and there are several champions on the team that, if/when fed, can dominate teamfights; even if another lane completely collapses. Gank-oriented champions such as Mao/Lee/J4/Malph can help get lanes fed however, and each lane has enough damage and killing power to turn most ganks into successful kills.
Try it some time in your next ranked or normal draft game. Watch your team's picks and the enemy picks, and tell yourself what each pick is good at, and what they're weak against.
What is an ally weak against? Can you counter that weakness?
What makes an enemy dangerous? Can you counter that strength, or exploit a weakness? Which is easier?
The more you practice this, the better you'll get at it. You'll also be able to understand picks and counterpicks more easily without requiring a guide. Eventually, it becomes almost intuitive.
The higher your ELO becomes, the more important it becomes to use champions that mesh and blend with your team. Your go-to picks wont always be the best decision, and your least favorite champions may become the key to changing the entire outcome of a game.
The countering process can be used in item selection as well. Not just in the "He does physical, I should build armor." sense either, but more to the tune of, "I don't peel very well, but they just picked Irelia, so I should rush Frozen Mallet to peel for my carry if she gets fed."
For me, I play Pantheon a lot. He's more of an offensive bruiser, designed for bursting squishies down with his devastating burst. However, more damage isn't always what I want. If, in that scenario, I had chosen Pantheon, and the enemy team then grabbed WW/Irelia, I would have to decide between rushing a Bloodthirster after Wriggle/Phage/Hex, or finishing Phage->Frozen Mallet. My decision depends entirely on how fed my carry/carries are in comparison to Warwick and Irelia. If both WW and Irelia are starved, a BT to end fights more decisively would benefit my team. If my carries are fed and WW/Irelia are at all farmed (not even fed, if they're just farmed it's enough) then Frozen Mallet becomes far more useful for making sure my squishies are safe.
You can also change up a build to include Ghostblade if you need chasing/killing power as a melee, or a Black Cleaver as AD if you have a physical damage dealers in top and jungle. Some options will be less popular than others, but can make a world of difference.
It's up to you to learn what champions and which items are optimal for each situation, but the more you practice and exercise that thought pattern, the more effective at it you'll become.
Even in Football, the saying goes; "The game is 80% mental and 20% physical."