I DID NOT WRITE THIS GUIDE.
After three years of playing league of legends I realized that I still haven't learned everything about league of legends and these little details were really important for me. So I wanted to share them with you.

Damage is classified into many types. To know more about your play style or what suits you the most you need to know what type of damage your champion deals. Some champions come with one type of damage and other champions come with a variety of them.

Attack damage

is a champion statistic which directly affects how much physical damage a champion does with its auto attacks and some abilities.

Physical damage

is a type of damage that champions' auto attacks, some abilities, minions, and turrets deal. Armor reduces incoming physical damage.

Magic damage

is a type of damage that most abilities, items, and on-hit effects deal. Magic resistance reduces incoming magic damage.

True damage

a type of damage that some abilities and spells deal. This damage cannot be reduced and always does exactly the value stated.

Basic Ability

All champions feature three basic abilities, which are available from level 1 to a maximum of five ranks. Basic abilities cannot be ranked higher than half the level of the champion (rounded up), meaning a new rank is available every odd single-digit level, and requiring level 9 to max any individual skill.

• Udyr has no ultimate ability, only four basic abilities.
• Elise, Jayce, Lee Sin, Quinn and Rengar each have six basic abilities.
• Including their evolved forms, Syndra, Kha'Zix, Karma and Viktor also have six basic abilities.

Innate Ability

A champion’s innate ability passively affects the champion for the entire match. Every champion has a unique one, and these abilities cannot be improved with ability points gained on level-up.

• Syndra features an innate ability with four different features.
• Vladimir and Akali feature two effects each.

Ultimate Ability

A champion's fourth and feature ability is their ultimate. Summoners cannot invest skill points into their ultimates until at least champion level 6 and cannot again until levels 11 and 16, to a maximum of three ranks.

• Nidalee's Aspect Of The Cougar replaces her basic abilities with a set of ultimate abilities. As such, Nidalee has access to four ultimate abilities; the most of any champion.
  While active, Nidalee has access to no basic abilities.
• Elise, Jayce and Karma are the only champions with access to their ultimate abilities at level one. Each may invest skill points into their ultimates at levels 6, 11 and 16, allowing it to reach rank 4.

Active Ability

This is the most abundant type of ability, having a one-time use effect, and are subject to a cool down before they are available for use again.

• On-hit Effect

  On-hit effects will trigger on a champion's auto attacks, but also some abilities.
  

• Apply on-hit effects

  These abilities are classified as auto attacks, and will apply on-hit effects instead of on-ability effects. To emphasize: these abilities do not apply spell vamp or Rylai's Crystal Scepter.
  • Ezreal's Mystic Shot.
  • Fiora's Blade Waltz (up to 5 times).
  • Fizz's Urchin Strike (apply on-ability effects too) Seastone Trident.
  • Gangplank's Parrrley (can critically strike, classified as a melee attack).
  • Irelia's Bladesurge.
  • Master Yi's Double Strike (two times).
  • Miss Fortune's Double Up (both hits).
  • Renekton's Ruthless Predator (two or three times, according to his Fury).
  • Shyvana's Twin Bite (two times, and to all targets hit in dragon form).
  • Twitch's Spray and Pray (on every target hit, can critically strike).
  • Warwick's Infinite Duress (up to 5 times, applies life steal despite being magic damage).

• Barrage ability

  A type of ability that can be cast several times and without mana cost before going on full cool down. There is brief cool down between multiple casts (generally 0.2-0.5 seconds, 2) and if too much time is wasted the additional casts are lost.
  • Ahri's Spirit Rush can be cast 3 times.
  • Darius's Noxian Guillotine can be cast again for 20 seconds after killing the target, can be cast multiple times.
  • Fiora's Lunge can be cast 2 times.
  • Irelia's Transcendent Blades can be cast 4 times.
  • Kha'Zix's Void Assault can be cast 2 times or 3 times if he has chosen to evolve this ability.
  • Riven's Broken Wings can be cast 3 times.
  • Rumble's Electro-Harpoon can be cast 2 times.
  • Xerath's Arcane Barrage can be cast 3 times.

• Self-Buffs

  These are abilities that grant passive effects once activated. These effects last either a fixed amount of time, such as Kog'Maw's Bio-Arcane Barrage, or last until a one-off component has been used, such as Rammus's Powerball.
  

• Stocked

  These abilities have a extremely low cool down but rely on "stock" to use. Stock is generated over time and there is a capacity unique to each skill to how many stocks can be stocked. When the ability is used, it uses up 1 Stock. Cool down reduction affects the time at which stock is generated.
  • Akali's Shadow Dance
    Corki's Missile Barrage
    Heimerdinger's H-28G Evolution Turret
    Teemo's Noxious Trap
    Zyra's Rampant Growth
    Vi's Relentless Force

Passive ability

These abilities are passive abilities that have persistent effects, and do not need to be activated per second. However, some passive abilities are unavailable under specific conditions, such as while the ability is on cool down ( Blitzcrank's Static Field) or upon taking damage ( Teemo's Move Quick). The ability will be activated again as soon as the specific condition has passed, i.e. the ability is off cool down, or no damage has been taken for a certain amount of time. These are often compared to innate abilities.

Toggle ability

These abilities are used by activating them and remain active with persistent effects until they are deactivated. The toggling of an ability is not considered an activation, for the purposes of Sheen or Force Pulse, but mana consumption of toggled abilities will stack Tear of the Goddess.

• Aatrox's Blood Thirst and Blood Price
• Amumu's Despair
• Ashe's Frost Shot
• Cho'Gath's Vorpal Spikes
• [[Dr. Mundo's Burning Agony
• Jinx's Switcheroo!
• Karthus's Defile
• Singed's Poison Trail
• Sion's Enrage
• Swain's Ravenous Flock
  Special toggles: These abilities are listed as being toggles, but have their own set of conditions: these abilities do count as activating an ability, and will toggle-off automatically if the champion moves too far away.
  • Anivia's Glacial Storm (will also toggle-off if she's disrupted)
  • Maokai's Vengeful Maelstrom

Stance ability

A type of ability currently unique to Udyr and Sona. Each stance has an individual cool down and a shared global cool down. Every stance provides an effect that lasts as long as the stance is active as well as an activation effect.

• Rammus's Defensive Ball Curl and Powerball are described as stances in their ability descriptions, and function like stances in that only one can be active simultaneously.
• Baron Nashor 's Voracious Corrosion and Wrath of the Ancients use a stance system.

Abilities have certain attributes that determine how they are used in game. These attributes include area, cool down, cost, effect, and range.

• Cool down All abilities have a cool down, a length of time after the use of the ability in which the ability cannot be used again. Cool down reduction reduces this time, to a maximum of 40% reduction of the ability's initial cool down.
  • Some champions have abilities that refresh/reduce the cooldown period.
  • Some abilities have a secondary active function. The ability goes on cooldown after the secondary function has been triggered or the window for triggering it expires.

• Cost

  Most abilities, but not all, have a specific cost associated with them. Generally abilities cost mana, though some champions use health, energy , or other resource mechanics. When the ability is used, the champion loses the cost of the ability. If the champion has less than the cost of the ability, the ability cannot be used and its HUD icon changes color.
  
  

• Targeting

  All abilities which affect a unit other than the champion casting it are targeted in some way. If an ability has a specific target it will hit, it is referred to as targeted. Other forms of targeting are referred to by their type:
  • Area of Effect (AoE) abilities can affect more than one target in an area. The affected area is generally circular, but conic or linear areas are also possible. Certain abilities, such as Diana's Crescent Strike, may have completely unique areas of effect.
  • Skill shots are projectile-based abilities, generally cast in a line away from the champions location, which only affect targets the projectile collides with.
  • Click-on abilities require a target and vision of it to cast. Most of these abilities are to either apply a buff or to use a strong projectile to assault the target. A simple click is all that is needed to start casting a Click-on at a target

• Cast time

  While most abilities have either an instant cast time or a slightly delayed instant cast of 0.5 seconds, there are several which prevent the caster from taking any other action while the ability is cast. Most of those, called channeled abilities, can be interrupted, either by the caster or by any form of Crowd Control (excluding Slows, Snares, and Blinds) applied by an enemy unit.

Every ability has an effect. These effects vary widely, but can generally be broken down as follows:

• Buffs

  Increase the target's statistics while active. Passive and Toggle abilities are most likely to have this type of effect. Active abilities which give buffs have higher bonuses than Passives or Toggles due to their limited duration. Some champions have AoE buffs for nearby allies, referred to as auras.

• Crowd Control

  This category includes all effects that reduce the fighting ability of enemy units. The page includes a table with notes on each.

• Damage

  Offensive abilities that deal damage. This damage can be either physical, magic, or true, and generally procs spell vamp, unless the description states it applies on-hit effects. Most damage-dealing abilities scale with a champion's attack damage, ability power, or both. Some abilities deal damage over time.

• Damage Reduction

  Reduces damage dealt to the target for the duration. This damage reduction does not apply to true damage and applies before reduction from armor or magic resistance.

• Gold

  Gives champions more gold than the base rate, either over time or on kill.

• Healing

  Heals a target. Healing generally scales with ability power. Support champions are most likely to have healing abilities, and are the only ones to have healing abilities which target a champion other than themselves. Several non-support champions have abilities that heal only themselves.

• Immunity

  Prevents certain types of crowd control from affecting the target, which is usually the champion using the ability.

• Invulnerability

  The target cannot be damaged for the duration. Currently only Kayle's Intervention provides a temporary invulnerability. Certain abilities also make units untargetable, such as Fizz's Playful / Trickster.

• Movement

  Moves the champion or the champion's target from place to place. This can be a dash, a blink, or a Teleport. Many of these abilities allow a champion to move through otherwise solid obstacles/terrain in a similar manner to the summoner spell Flash.

• Resurrection

  Brings target back to life if reduced to below 0 health, though other conditions may apply.

• Shield

  Absorbs a certain amount of damage for the target, in place of losing health.

• Stealth

  Target becomes unseen and untargetable until revealed or duration expires. The page contains further information, including means of detecting stealthed champions.