Gameplay Mechanics

Stack Items
All stats from items will stack additively except for those that have a UNIQUE ability. For instance, the Infinity Edge item has the following stats:
 * +80 DMG
 * +20% Crit
 * UNIQUE Passive: Critical hits now deal 250% damage instead of 200%.

If you were to pick up two Infinity Edges, you would have the following stats:
 * +160 DMG
 * +40% Crit
 * UNIQUE Passive: Critical hits now deal 250% damage instead of 200%.

Note that both the damage and critical chance stack additively, but because the passive to the Infinity Edge is UNIQUE, you cannot be affected by that more than once.

Item auras
If you and a teammate both have the same item, you will be affected by the aura twice. As an example, at the start of the game you purchase Mana Manipulator. This item gives a mana regeneration to yourself and allies nearby. If you were to go with a teammate who also purchased Mana Manipulator, both of you would be affected by this aura twice. However, if you had a third teammate that did not have the Mana Manipulator they would only be affected by one aura.

Cooldown reduction
Cooldown reduction works additively. If you have a 9% cooldown reduction from masteries, and a 10% cooldown reduction from Stinger (an item ingame) you will have a 19% cooldown reduction. However, cooldown reduction caps at 40%. This means that you can't get more than 40% cooldown reduction.

Dodge
Dodge works with diminishing returns. As an example, let's say you have 10% dodge in your runes.
 * 10% dodge.

You grab Ninja Tabi, which gives 11% dodge.
 * 11% dodge + (89 * .1) = 8.9% dodge = For a total of 19.9% dodge. (Note that the 89 comes from the percent remaining from the previous dodge percentages have been calculated).

You then get Phantom Dancer, which gives 20% dodge.
 * 20% dodge + (80 * .11) = 8.8% dodge + (71.2 * .1) = 7.12% dodge = For a total of 35.92% dodge.

Spell Dodge
You can't dodge spells. The only way to not receive damage from spells is to be spell immune from one of these:
 * Banshee's Veil (blocks one spell every 30 seconds)
 * Sivir's Spell Shield
 * Morgana's Black Shield
 * Boost
 * Judicator's Invulnerabilty (note that unlike the others, while this one blocks spell damage, anything secondary like a slow would still happen)

Levels of boots movement
Level 1 adds 50, Level 2 adds 70, Level 3 adds 90.

Movement Modifiers
Your base movement: 300. You add boots first, always boots first, so if you have boots added - Boots 1 give a flat 50 movement, boots 2 give a flat 70 movement, boots 3 give a flat 90 movement.

Let's say you get boots 2. That's 370 movement. Then, you get 35% movement speed buff from items or runes or masteries or buffs: that 370 is multipled by 1.35, or 499.5 movement speed. If this is the only thing affecting your movement speed, the diminishing returns formula kicks in.

Now, let's say you get slowed by 38% (ashe arrows). What happens is the ORIGINAL 499.5 is multipled by .62, and you get 309.69 movement speed. Because 309 is not above or below dimineshing returns, you stay at that speed.

Diminishing movement returns
For each point of movement you would have above 475, that amount is reduced by 50%. So if your final movement speed was 733, it would be reduced to 475 + (733-475)*0.5 = 604. For each point of movement you would have above 400, it is reduced by 20%. So if your speed after all mods was 430, you would end with 400 + 30 * 0.8 = 424.

Lifesteal
Lifesteal is affected by armor. If you hit for 100, they have 20% reduction, you hit for 80, you have 10% lifesteal you gain 8 hp. Lifesteal stacks additively and doesn't have a cap. This means that you could get over 100% lifesteal.

Armor and Magic Resistance
Every 1 armor means the damage it takes to kill you is extended by 1% of your hitpoints. At 100 armor, it takes 100% more damage to kill you, so it requires double damage and you're taking half-damage. At 300 armor you're taking 25% damage, etc.

The damage it takes to kill you is scaling linearly. If you have 1000 hitpoints, then each point of armor means you can take 10 more damage before dying. And this is true no matter how much armor you have (aside from rounding errors). So in that sense, it's linear, and there are no diminishing returns.

Magic resistance works in the exact same fashion, except it does so against spells only. There is no overlap between armor and magic resistance at all. Armor would have no impact on spells, in the same fashion Magic Resistance would have no impact on physical attacks.

In Game Statistics
When you are in-game, there are four stats at the bottom (Attack, Ability Power, Movement Speed, Armor). To see other, less common, statistics like Dodge or Magic Resistance, press 'C'.

ELO Rating
ELO is the ranking system used in LoL. The way is works is that when you get matched up against a team, your team will be expected to win or expected to lose, depending on your ELO.

Ex.

Team A - 1250 ELO Ranking Team B - 1350 ELO Ranking

In this scenario, Team B is expected to win. If they win, they will gain less ELO because they were the stronger team going in.

Team A - 1250 -> 1242 Team B - 1350 -> 1358

However, should Team A win, they will gain more points than usual because it was an upset.

Team A - 1250 -> 1263 Team B - 1350 -> 1337

Note that this is acting as if the entire team has their own ELO, what actually happens is that a team's ELO is considered depending upon the players inside and other factors. As an example:

A pre-made comes in with these players:

Noob - 1000 N0ob - 1000 Noobie - 1000 Newbie - 1000 Newskis - 1000

Now, this team doesn't have a 1000 point rating when it gets put into the pool. What happens is that they get a slight modification (between 25 and 200 points, I think) because they are a premade, and are expected to be stronger than simple pubs. So, even though all the players are 1000 ranked, the actual team would probably be ranked 1100-1150.

There isn't any way to see your ELO ranking from Normal games. The idea there is that the matchmaking is for fun, and that you shouldn't be worried about losing. When Ranked games come in, those are where the ladders and competitive play will be shown.