Runes and Masteries

These can be found by pressing the Summoner Profile button
Runes

Runes, which are assembled on rune pages, allow you to build a set of bonus statistics that can be applied to any champion that you play.

This is an empty rune page at level 1.
An individual rune only offers a small stat bonus, but once you have a full or nearly full rune set they can add up to make a noticeable difference.

There are 4 types of runes that specialize in particular types of statistics.

Marks: Strongest runes of this type are Offensive statistics.
Seals: Strongest runes of this type are Defensive statistics
Glyphs: Strongest runes of this type are Ability statistics
Quintessence: Strongest of all runes; but in total you can only have 3.

There are however a large amount of runes that do not 'match' the rune type. Allowing you build up stats in their non-optimal areas. This can be useful for hard to come by stats in game or stats that you want but you don't want to buy items for.

Each summoner level will unlock a new slot on the rune page, at level 30 you'll be able to equip up to 9 marks, 9 seals, 9 glyphs and 3 quitessences!

This is a full rune set at level 30.
Runes will have an a glowing border, when attached to a rune page, that represents the category the stat is strongest in. For instance you'll see above that my glyphs have a yellow border. That is because the stat that they offer, mana regen, is considered a defensive stat. The strongest non-quintessence runes available for mana regen are seals.

Runes are available in 3 tiers, each tier offering stronger runes than the last. Summoner levels 1-9 can only purchase tier 1 runes. Summoner levels 10-19 tier 2. And 20-30 tier 3.

Same rune, different tiers.
Runes are purchasable through the game store in exchange for influence points. Tier 2 runes are generally viewed as a waste because they will be outclassed by tier 3 runes and don't offer enough of a statistic boost from tier one to be worth the increased IP cost.

During the holidays Riot will occasionally offer an array of "tier 2.5" runes which are more expensive than tier 2 runes but significantly less expensive than tier 3. For all extensive purposes they are actually tier 2, meaning you need to be at least level 10 to unlock them.

Look at the middle rune, in all of it's glory.
As you can see from the image above, the holiday rune offers nearly tier 3 value for half of the price. And you can get this as low as level 10 if you're determined enough to save up the IP.

In champion select before the game starts is where you can choose which rune page to use.
 All accounts start with 2 rune pages; you can buy additional pages or a bundle of 7 from the store.

Masteries

If you've played WoW before, this should look very familiar
You get one mastery point per summoner level to a maximum of 30. Your points may be spent in any distribution between the three mastery trees, and can be reset at no expense at any time out-of-game.

Masteries offer a variety of bonuses that cannot be obtained through runes. While some masteries are flat statistic gains, there are quite a few masteries that grant a special effect or increase the effectiveness of a particular summoner spell.

Unlike runes you only have one set of masteries and they will automagically be applied to your champion. It is possible to reset your masteries in champion select though!

Click directly below the rune page drop-down.
While it is possible to reset your masteries in champion-select you should keep an eye on the timer in the top left of the screen. If that timer runs out before you press 'Save Masteries' you will have no masteries at all.