A wise man learns from instruction but a fool only hears many words.
In other words, think about what you read here.
This guide teaches no special builds or hidden techniques only how to think, plan ahead and thereby win.
How well you do is up to you - you must apply yourself to a thing to profit from it.
This guide is for the new player and the experienced master alike. I am not a master myself but the simple principles I will cover apply to all equally.
Strategy - thinking ahead
To make a good decision you must be informed. Study the champions. Know their strengths.
No champion has a severe weakness that cannot be covered with the right gear (at the time of this writing) so focus on knowing champions unique abilities and strong points.
You must know your enemy to succeed.
Learn from others. Read champion guides and think about how the information you find works.
You may find a real gem with a little effort.
Study the available gear. Know what items do what.
Did you know there is an item which can take 1/3 of an enemy's health when activated?
Watch how other players play the game. Especially after a match - look at the builds of the players with the most kills. Usually their success lies in having a good build and knowing their champion thoroughly.
If you have a decent level of knowledge of these things, you can make an intelligent decision in terms of strategy.
"Decisions, decisions, decisions..."
First decision - choosing a ROLE.
Before selecting a champion, decide what role you will fill. Talk to your team. Help round out what the team needs. Most champions can fill several roles depending on their equipment.
Example: Kog' Maw
- good enough 'mage' but excellent damage-per-second if you use the right gear and abilities.
Second decision - choosing a CHAMPION
You have your assigned role, if you can play many of champions then you might want to let the other players make their choices first and decide based of their choices.
If you are limited in what champions you can handle, let the team know so that they can adapt to your limitation.
Here's an example - champion BlitzCrank with a player who knows how to use the 'Rocket Grab' skill well can easily dominate a lane if paired with a DPS ranged role who can also slow down or stun the target, even a little.
Final decisions - choosing spells, runes and masteries.
These decisions are easy enough if you know your way around them already, simply pick in accordance with your role. I tend to favor DPS roles and since I fill that role with a slow moving champion I favor teleport to move around the map quicker and ghost for escaping and chasing.
So you've picked a champ, runes, masteries and spells, you've locked in and now you're summoning.
This is a good time begin considering TACTICS.
Tactics - thinking further ahead
Generaly speaking, tactics are the decisions you make on the field... actually, you can make most of them ahead of time if you know your champ and build well enough.
Example - in my favored role I know that one of the things I excel at is taking down tank champions. In a team brawl I will almost certainly prioritize my targets like so:
1. weakened champs / problem champs (depending on the situation)
2. runners - they are NOT getting away.
3. tanks - usually a very small threat so they are actually low on my list.
Another example - If I've just helped to take down a tower the enemy will probably arrive there in force shortly after so I've already set in my head to get out of the area after a tower goes down, usually.
Often the first part of tactics you will consciously consider is the matter of the other team.
During summoning you can see what champions the other team is bringing to the field. Question is, how will they be handled? It helps to bear in mind which champions are on free rotation at the time. Players using them might be completely unfamiliar with the champion and therefore an easy target. If the enemy has alot of mages, you might want some magic resist. If you see common dps champs (especially ranged ones), expect them to have the middle lane. If you spot your bane (that champion you just can't deal with) make it a point to NOT get matched against that champ or you will just end up feeding them and making the situation worse.
There's more to consider - what gear should you use on the field this time?
It's very much situational. Your build may call for particular items but if your quarry keeps escaping, maybe you should invest in Phage to help hold 'em down and/or get some help from a team mate. If your enemy ISN'T running (yet) skip the phage and go for Madred's Bloodrazors to tear through their hp faster. These are just examples of situational choices, not recommendations.
Here's what alot of newer players miss though - you can look and see what the enemy is equipping themselves with. If you know your stuff you can second guess what their build plan is and thwart them.
Winning
League of Legends is so complex (and growing bi-weekly) that there's no way I can write a comprehensive guide to all the little tips and tricks that will help ensure you win. What I can do though, is tell you how to keep on top of the game.
GAME CHANGERS
These are usually little things, things that change the overall way the game is played. Usually these changes come in the form of an update. Maybe it's a new item, or a severe nerfing, or that new champion.
At the time of this writing LoL is about a month or so out from a major, game changing update. Previously, tanks were a vital part of winning teams. After the change, tanks were roadkill for anyone who got in on what happened. Mages were the new ruling role. That trend has since played out and re-balanced itself with most tanks re-appearing as damage heavy builds (off-tanks).
Always study an update thoroughly and think about the implications.
CHANGING TIDE
Whenever the 'metagame' changes (the over all pattern of wining strategy) most everyone piles onto it early on. Then there's a second shift as the smart players adapt. Then there's another shift as slower players adapt and the top predators adapt further. That's how the game play flows. Staying on top of it can be a little tricky and you have to be thinking ahead for every game.
That about does it. Winning is simple but it requires study, preparation, cooperation and thinking on your feet.
Having the cooperation of your team helps alot but in some cases you can survive a couple of idiots.