This is a guide meant for bronze level or even silver level players that don't have some of the basic information of League Of Legends in order to climb the ladders and to be efficient in what they do. I will include itemization basics for each lane, type of laners for each role, and how each champion fits into a certain role. At the end I will go through the basic support,top,adc,mid and jungle pages that everyone should have before diving into specifics for champions.
I will also include some basic objective based ideas to keep in mind to help you snowball your leads.
Some resources to find out maybe more specifics are as such:
http://www.lolpro.com/
http://www.probuilds.net/
http://leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki
Or MobaFire; they have great c9 builds

This guide is a very very general guide built on basics.

I've formatted the guide as such:

At the top, clicking your position I will show basic items ingame that you would build on various champions (Items that are typically viable). I've given you the basic mastery page for the specific roles. Standard/ cheap rune page for your role. and in the Vs. Champion tab I added the various champions that you should play in the respective roles and their difficulty level.

Theory:

You'll be amazed how easily you can carry a game on top lane alone. Forever, this role was seen as the "island" role as you do your own thing for the most part until the teleport meta was introduced which changed everything. Now, on a dime, you must TP in on a fight and change the whole game by doing so.

There are three types of laners for this lane each with their own objectives and roles within the team. Of course this is all very general, but it might help you see what the purpose of top Maokai actually are for example.

Tanks: This shouldn't be too hard for you to understand, they absorb all the damage they can. They are champions such as Dr.Mundo, Maokai and Trundle. They are trying to disrupt the enemy team through crowd control and overall their pure massive models. Your goal is not to win lane, but to live it. You will want CS as everyone does in your laning phase, but most importantly exp. You can initiate, but mostly you just want the entire team to focus on you and let your carries do all the work.

Split pushers: Champions such as Shen, Zed and Tryndamere. Their goals is to constantly split push and force the enemies to come to you, while your team can take more important objectives. It's critical you take TP so you can split push yet still be able to come in on a fight.

Brawler: This is where you put the carry in the top laner. This is split from AD and AP alike, but they want to be in team-fights just as all the other top lane roles but they are more team orientated. They deal damage while still providing utility. Champions such as Rumble, Shyvanna, Trundle, Riven, Jax, Gnar... most top laners fall in this role to say the least. You need to find the balance of acquiring CS through split push, team objectives, tanking yet dealing damage. Obviously the hardest to master due to all these requirements, but most rewarding.

Spirit Visage: Healing/tanky/MR/CDR
Warmogs: Pure HP/Regen
Randuin': Armor/Active
Frozen Heart: Anti AD/Armor/CDR/Aura
Locket: Aura/Overall Tanky/Team

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Hydra: Split push/sustain/combat effectiveness
Bloodthirster: RARE/Carry positions(jax,riven etc)/sustain/damage
Black Cleaver: Tanky damage dealing
Maw: MR/damage


You want to balance your carry with tanky items because typically, and there are exceptions, you still need to get tanky and will be one of the only tanks. I suggest only really building one aggressive item if you're an off tank type champion. Build accordingly to your lane of course at first:
VS AD: Randuin's/Hydra/Frozen Heart
VS AP:Maw/spirit visage

And then depending on what players are fed on the team you just stack armor and magic resist accordingly.

Theory:
There are two types of REAL junglers in this game.

Gankers: These are the most common kinds, they focus on the lanes, and trying to influence the lanes themselves. This kind requires the player to be intuitive and have game experience to know where to counter-gank the enemy and where to apply their pressure. The biggest key is applying pressure where it will yield the most influence on the game. Champions such as jarvan, rammus and lee sin excel at this.

Control Junglers: These are not as common and even looked down upon in the lower tiers. This is where you deny the enemy jungler exp and gold in their jungle, keeping constant vision of the enemy jungler through wards to deny ganks form ever being successful. Junglers such as Nunu, Udyr and shyvanna do this well.

Tips:
You need to pay attention. Look for when the players go to ward their lanes, so you know if it's warded or not. Put yourself in the position to make a good gank happen. Optimization is key for this role as you have sparse resources and have to carry the early game with it.

This is the hardest role to itemize because you literally have to build according to what yur team needs and what the enemy team has.

Currently as of 08/12/2014 you should always get trailblazer with the exception of a select few champions. I literally mean everyone except like warwick. If you don't you are not being optimal. Always upgrade it before buying anything else. Upgrade it logically thinking about what you as a jungler want to do and what your champion is capable of doing.

If you need damage:

Black Clever: Always a safe choice because it hits hard and still keeps you decently tanky.

Maw: Helps give you straight AD if your champion scales well with it (look at champion notes on lolwiki to see scalings) as well as protects you from AP with the MR.

Last Whisperer: Essentially a less tanky Black Clever with more damage so again, if you scale really well with AD itemization, pick this up for quick damage. Of course sacrificing tankyness.

Banshee's veil: More of a midgame-late game. If they are focusing you for the initiation and you cant get locked down, this will help you.

Randuin's/Locket: Buy one of these items in every game (usually Randuin's for active) if you are initiating, get Randuin's. If you're kiting more (rare) get locket.

Righteous glory: Really good for really tanky junglers that initiate because it speeds your team up upon activation and exploding slowing everyone around you.

ALWAYS WARD. Lee sin(for jump and why not) and Control junglers should get sight-stone ASAP

There are three general types of midlaning champions.
1. Assassins
2. Mages
3. Roamers

Assassins are like fizz, zed and yasuo. Typically they use ad and they look for picks and have tremendous 1v1 capability. Your job is to eliminate one threat and usually die or peel away from a fight. You have to kill the top damage dealer or whoever your team decides. You look for picks in the jungle and swaying the game in your favor by split pushing and forcing the enemy to focus on you.

Mages are like Anivia, Veigar, Orianna and Azir. Your goal is to do steady, high damage over a period of time as well as adding a significant utility to the team. They are the easiest because usually their kits are great for the team and great for team fighting compositions and objective control. You look to carry with your team behind you and forcing the other team into weird positions and focusing questions.

Roamers like ahri, twisted fate and to a degree assassin type champions. Their goal is to not necessarily destroy their lanes, but the other lanes around them. They typically need to get their team moving by using rotations to basically outplay the enemy team in an elaborate game of chess. They excel at objective control and siege compositions as they typically have long range abilities, sustain yet team fighting capabilities. They are kind of good at everything but obvious weaknesses in their kits.

Mid lane depends on which role you're going for in the mid lane and whether yo're AD and AP of course, but i'll cover AP since all AD champions require specific builds.

Morellonomicon/Athena's Grail/ Seraph's Embrace: In a given choice, typically you have to choose one of the three items to itemize. Morello's is really good right now due to it being cost effective and giving CDR but if you feel you need more MR in the matchup you should go the grail. And if you're feeling late game you're going to get jumped on, seraph's embrace is fine. I recommend not buying that item as it takes too long to ramp up for Mid Laners.

Zhonya's: Very powerful item, gives good AP, armor and the active is great if the enmy engages directly on you. Almost a must on every champion that uses AP in the mid.

Deathfire's grasp: This item will increase your burst potential. Good for veigar, syndra etc that want to burst someone in a big combo. Just make sure you remember to use it before all your other spells.

Deathcap/Void staff: Big magic dealers. If the enemy team starts stacking MR, get void staff to negate it. If you already have a lot of AP, Deathcap will just escalate it even more plain and simple. Both Mage staples.

Lich bane: Good for Fizz and Twsited Fate msotly. Good for anyone that uses auto attacks as it empowers the next auto attack you do after an ability. Very powerful item on some champions, nearly useless on others.

Theory:

In this meta, you cannot die. You are the primary source of damage at late game. You are the team's carry overall. Your goal is to be safe, and to deal damage. There is no point on you getting all the cs you can, and getting these leads if you don't do anything in a fight. So your positioning has to be perfect. You have to position yourself to maximize damage dealt, but limit damage taken. It's a hard job. But if you do it well, you'll carry your team regardless of their skill.

This is incredibly hard, yet simple to pull off. I listed all the items off, yet there are recommendations.
You don't want to really need to build lifesteal until later on. Don't do it erly or you will limit your damage output early on especially in laning phase. You don't get enough return value for things like bloodthirtster.

Infinity edge is the traditonal ADC item, it gives you everything you want.

Build trinity force if and only if you are so ridiculously ahead you can't lose, or if you're corki.
Build Last Whisperer when the enmy team starts stacking Armor, otherwise there are better items to build.

Build Yoummu's if you're running a seige type composition.
Statik shiv for split push comp + it's pretty good overall Helps you get gold really easily mid game too.

GA/Banshee's veil/Merc Scimitar: You need to build one of these items as last item. GA if you expect extended teamfights that could go either way. Banshee's veil if you're getting engaged on too often. Merc Scimitar if they have incredibly hard CC you need to get out of.

Game going past 60 minutes? Sell boots and get Zepher.

Your job is to protect everything in the game. That is your purpose. To do this you need to ward, you need to build accordingly and play accordingly. You either hard engage with a tanky champion on the other team, or you're peeling for your ADC. Peeling is when you basically take appropriate steps to stop the enemy team from just jumping on your Allies and destroying him, but instead getting in their way.
The biggest thing is learning how, when and where to ward. I will link a picture to give you a very general comprehension of it. You also need to sweep ward where they would place them to deny vision. The more vision you have over the enemy, the better. It's up to you to win the vision war.

Starting Items:
Relic Shield + Health Potion *3 + Mana Potion (Tank start)
OR
spelltheifs edge + Health Potion *3 + Mana Potion (Utility start)

First buy:

Sightstone

After that it depends on what you`re playing.
If you`re playing utility type champions, next you`ll want Mikael`s Cruicble to help your ADC with the active if they get locked up + mana regen. (Morgana should get Zhonya`s first)
Then Zhonya`s or Mikael`s Cricible and vice versa or Talisman of Ascention (Sell spell theifs, it`s no good anymore).

If you`re tanky then build The face of the mountain into Randiuns for the active when you initiate and Locket for the peel and cheap aura item.