TL;DR[]
You gain sight of all the things that your allies have sight of. Terrain and brushes restrict what you can see. Some champions can enter stealth. Stealthed units can't be seen except by special mechanics. Wards are crucial to winning games.
Now You See Me...[]
One of the most important concepts in League of Legends is vision. You here terms thrown around like "Vision Control, "Map Control," and "Map Vision," and they're all very closely related to the same thing: How much of the map are you able to see?
Now, when we say "see," we don't necessarily mean on the main screen. Let's take a brief detour and discuss the minimap.
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Stealth[]
Stealthed units are units that are invisible even if a champion or team has sight of their position. Stealthed units can be revealed by certain mechanics that provide true sight. There are several units in the game that can be stealthed. Some champions can enter stealth, a few champions can lay stealthed traps, and all
Stealth Ward and wards issued from
Warding Totem are stealthed.
Stealth can be broken into two classes. One type of stealth is combat oriented for engaging on opponents that may not be expecting it and can be triggered more than once within a skirmish. The other kind of stealth can be used only to enter or exit a fight. These two classes of stealth are called invisibility and camouflage respectively. Damaging a stealthed unit of either type will grant a shimmer of their character for a brief moment.
Invisibility
Invisibility is stealth that lasts a short duration, can be used to reposition within as single skirmish or team fight. Invisible units cannot be detected by control wards. Invisible champions also can not travel long distances before the effects of the invisibility wear off. 
Talon's ultimate 
Shadow Assault is a short term example of invisibility. Unless damaged by a true sight ability of the enemy team's, Talon will be able to use this ability and for a short duration be able to move around an enemy completely undetected.
Camouflage
Camouflage is stealth that lasts a long/moderate duration. Camouflaged units can be revealed by control wards, but stealth wards and trinket yellow or blue wards will be completely unable to see camouflaged units within their range unless those units are in combat. For example, 
Evelynn's passive 
Demon Shade hides her until an enemy champion is in nearby proximity, at which point she is revealed to the enemy.
True Sight
There are a few mechanics in the game that grant true sight of an area of a map, revealing camouflaged units. The most common are control wards, usually referred to as red wards (because they're red). They are called control wards because in addition to revealing a small area and possibly camouflaged units, they can also disable regular
Stealth Ward, traps and trinket wards. We'll talk about wards a bit later on in this page, so for now just know that red wards give true sight within their radius.
Sight vs Vision
Sight will always mean the ability to see non-stealthed units. "Vision" is sometimes used to mean the same thing as "sight," and sometimes used to mean the same thing as "true sight." To avoid confusion, we will use "vision" as a catch-all term to mean things related to what you can and can't see, and when specifying anything related to stealth, we will use the terms "sight" and "true sight."
Mechanics that Provide Sight[]
There are several ways for a player to gain sight of an area:
Innate[]
- Every champion has sight of all locations in line-of-sight within a certain radius (when
Rek'Sai is 
Burrowed, her radius of sight is significantly reduced) - Every champion has sight of all locations that any allied units have sight of, except in a few special circumstances, such as
Nocturne's 
Paranoia, 
Graves's 
Smokescreen, and 
Quinn's 
Smokescreen. - Every minion has sight of all locations in line-of-sight within a certain radius
Spells and Items[]
- Stealth Ward have sight of all locations in line-of-sight within a certain radius
- Certain spells and item actives can reveal all locations within a radius of a point on the map, without line-of-sight restrictions. Examples:
Farsight Alteration and
Ashe's 
Hawkshot - Certain spells can cause a team to have sight of an enemy champion and all units near that champion for a short duration. Example:
Lee Sin's 
Tempest.
Jungle Camps[]
- Killing the Rift Scuttler provides vision in an area in front of either Dragon or Baron.
Jungle Plants[]
- Autoattacking the Scryer's Bloom plant will grant vision in a cone exending out from the plant location itself over a large area of the map revealing camouflaged units, invisible traps, and wards.
Mechanics that Provide True Sight[]
- Control Wards
- Oracle Lens
- Scryer's Bloom
Mechanics that Prohibit Sight[]
There are several mechanics that stop a champion from having sight of an area.
- Terrain blocks line-of-sight.
- The entrance to brushes blocks line-of-sight. The exit of brushes does not. So you can see out of a bush, but not into it.
- As mentioned above, certain abilities, such as Nocturne's Paranoia and Graves's Smokescreen.
- A
Oracle Lens removes the sight that a team gains from its Sight Wards and all stealthed traps for a short duration. - Rek'Sai's Burrow significantly decreases her own sight radius, but has other benefits, including a "radar" sense that reveals the locations of moving enemy units but no other information about them within a large radius centered around her.
Vision Score[]
The Vision Score is a non gameplay-impacting statistic (it's just for viewers' and players' knowledge) which allows players to better understand their contribution when it comes to using wards or removing enemy wards from the map. As stated below:
"Vision Score is a loose measurement of vision game contribution, and can be ballparked as "about 1 point per minute of ward lifetime I'm responsible for providing/denying." It tends to be in the 5-150 range." - Riot Cosantoir
Wards[]
There are 4 types of wards: Control Wards (or Red Wards), Green Wards (or Stealth Wards or Sight Wards), Yellow wards (or trinket wards or yellow trinket), and Blue Wards.
Control Ward[]
- Control Wards are visible by sight, and they reveal camouflaged units and invisible traps or wards.
- Control Wards disable nearby green wards and yellow or blue trinket wards, denying the vision typically granted by these items.
- Control Wards last until they are destroyed by an enemy team, or the champion that owns the Control Ward places a new one.
- Each champion may only have one active Control Ward on the map at a time.
- Control Wards can be targeted by champion basic attacks. Each basic attack does 1 point of damage to them.
- Control Wards have 4 HP total.
- Control Wards are worth 30 gold for the player that destroyed them.
- Control Wards cost 75 gold in the shop to purchase.
Green Wards[]
- Green wards are invisible to sight, visible only to true sight. Green wards provide sight, but not true sight.
- Green wards last for up to three minutes or until destroyed or until a champion owning three green wards on the map places a fourth, at which time the first one placed is removed.
- Each champion may have up to three green wards on the map at a time.
Warding Totem wards count toward this limit. - Green wards can be targeted by champion basic attacks. Each basic attack does 1 point of damage to them.
- Green wards have 3 HP total.
- Green wards are revealed and disabled by
Oracle Lens. - Green wards are worth 30 gold for the player that destroys them.
- Green wards can only be acquired through the shop by collecting 500 gold while having any item among
Ancient Coin,
Spellthief's Edge, or
Relic Shield or their upgrades in your inventory, and purchasing
Remnant of the Ascended,
Remnant of the Watchers, or
Remnant of the Aspect; this will upgrade the latter into the
Eye of Ascension,
Eye of the Watchers and
Eye of the Aspect respectively. You can only purchase one gold income/vision item.
Trinkets[]
There are four types of trinkets: Red, Upgraded Red, Blue, and Yellow. Red and yellow are available at the start of the game, and upon reaching level 9, a player may change to blue or upgraded red. It is free to exchange trinkets other than a cooldown penalty at the time of switching. Choice of trinket between Red, Blue, and Yellow is an important strategic decision that teams make, and most players will exchange their trinket at least one time during a game.
Warding Totem[]
The Warding Totem (usually just called "yellow trinket" or "yellow ward") is available at level 1. It holds up to two charges, and you can consume a charge by placing a ward on the ground. These wards last for less time than normal
Stealth Wards but are otherwise identical.
- Yellow wards are invisible to sight, visible only to true sight. Yellow wards provide side, but not true sight.
- Yellow wards last for 90 - 180 (based on level)
- Yellow wards are trinkets, which recharge over time. Yellow wards have a 240 - 120 (based on level) seconds recharge time for each charge.
- Yellow wards can be purchased for free at the time the game begins.
- Yellow wards can be targeted by champion basic attacks. Each basic attack does 1 point of damage to them.
- Yellow wards have 3 HP total.
- Yellow wards are revealed and disabled by
Oracle Lens. - Yellow wards are worth 10 gold for the player that destroys them.
Farsight Alteration[]
The Farsight Alteration (aka "blue trinket" or "blue ward") is available at level 9. Technically blue is the upgrade of yellow, but they're very different from each other and so a player may or may not choose to make the change. A blue trinket can reveal an area about equivalent to that of a ward, but at a great distance from the caster. The reveal lasts for 2 seconds. It also leaves behind a permanent ward with 1 HP that's visible to the enemy team and has a much smaller sight radius.
- Blue wards are visible to sight. Blue wards grant sight in a shorter range than yellow, green or red wards, however they initially provide a much larger radius upon placement.
- Blue wards can be placed at extreme ranges, much longer distances between the player and blue ward can be achieved than with other wards such as yellow wards, green wards or red wards.
- Blue wards can only be upgraded at the shop at level 9 and above.
- Blue wards have a scaling recharge time 148 seconds at level 9, down to 99 seconds at level 18. Can only contain one charge at a time.
- Blue wards will stay on the map until destroyed by an enemy player.
- Blue wards can be targeted by champion basic attacks. Each basic attack does 1 point of damage to them.
- Blue wards have 1 HP total.
- Blue wards are worth 15 gold for the player that destroys them.
Oracle Lens[]
This trinket is for clearing (disabling and then killing) wards. Using this trinket reveals anything that a pink ward can reveal (other than champions) and disables everything that it reveals. Oracle Lens covers a wide area and is centered around the owner, and moves as the champion moves. It lasts 10 seconds and has a 90 - 60 (based on level) seconds cooldown.