This is a general guide for picking runes. Most people think that runes don't matter, but they are game changing. The difference between an amumu with aftershock and an amumu with no runes is insane.

There are 5 type of runes, and they each have their own specialties

Inspiration: gives utility and gold efficiency
Resolve: tankiness and protection
Precision: sustained damage
Sorcery: spell damage and ability modifier
Domination: burst damage and snowball

Inspiration has 3 keystones: Glacial Augment, Prototype Omnistone, and Open Spellbook.

Glacial Augment: Great for running targets down or kiting. Neeko top builds this. Item abilities that slow activate this (everfrost, chemtank, randuins, etc.)

Prototype Omnistone: swap keystones every few seconds. Not many champions can actually utilize this, but the ones who do are either ranged or have the sustain and mobility to trade frequently. Dark harvest souls increase the effects of the other runes. You can also use many keystones within a short timeframe, which gives it the edge over other runes (for example, it is possible to get dark harvest twice in a row with basically no cooldown, allowing 2 soul within a few seconds)

Open Spellbook: can swap summoner spells. Very useful for blind pick. For example, veigar mid you would pick this so if they have a zed you can swap one of your spells for exhaust. Allows more summoner spells than you would normally be able to use at the cost of a keystone.

Contraption: Hexflash, free boots, perfect timing

Hexflash: good for engage. Worth it if you get a single kill, since you chose this instead of free boots

Free boots: ironically, don't get this if you need movement early on as it stops you from being able to buy early boots. Getting this usually means you are in a farm lane or scale and want to hit your core and not have to buy boots (eg. Nasus).

Perfect timing: free stopwatch halfway into the game. reduces zhonyas cost by 250. Use it before crafting into zhonyas for full use. If using it stops you from getting killed, it's worth it because the 300 gold you got from denying a kill plus 250 gold worth makes it a better choice than the others. Try to only build on champions that use stopwatch items (GA, zhonyas)

Tomorrow: debt, dematerializer, biscuits

debt: allows you to hit item spikes faster but costs more gold in the long run. Good on supports and maybe ARAM

dematerializer: allows you to get cannons without taking poke (good idea as something like nasus vs teemo). Using on a cannon wave can allow you to fast push. Using on a minion a champion is teleporting to will cancel the teleport.

biscuits: get 3 biscuits (30% missing hp and mana healing along with 150 max mana), you can also sell them for 30 gold each. Would not recommend selling them. While most people use it early, since it scales with hp you can save them for laater on to survive ignite.

beyond: cosmic insight, approach velocity, time warp

cosmic insight: lower summoner spell cooldown. Good on people reliant on summoner spells. More useful the longer your summoner spell cooldowns are, anti synergy with nimbus cloak.

approach velocity: mini glacial augment, but it speeds you up and only towards enemies you slow. Good on Ashe and melee people who have ranged slows like nasus and trundle.

Time warp: applies half of a potion (or biscuit) instantly. Use with champions that start corruption. save potion charges until mid fight to bait them into a disadvantageous position. If they have ignite, however, use it before they cast ignite because of the reduced healing. Also grants 5% movement speed so you can chase.

Keystone: pta, lethal tempo, fleet, conq

pta: 3 attacks in a row deal damage and increase damage dealt to that champion. good on champions that require 3 auto attacks to deal large damage (vayne, kindred), as the increase applies to all subsequent effect. Low scaling power but large damage early

lethal: after damaging an enemy champion gain a lot of attack speed. Make to realize the 1.5 second difference between the time of attack and the attack speed gain. allows you to go above the attack speed limit. Good on tryndamere and ashe or other people with much damage on on-hit effects. Better scaling that hail of blades, since it lasts up to 6 seconds. Not good on assassin types because of the 1.5 second delay

Fleet: after walking a bit gain energized attack that heals and increases move speed. Good for sustain and disengage. Good as or against ranged poke.

Conq: gain damage the more you attack. At max stacks gain healing for a percentage of the damage you deal. Very strong. at max stacks gives 500 gold worth of damage alone, not counting omnivamp. Good for people who exceed at long trades (darius, garen). Not as useful for adc as they already build lots of damage and healing. Stacks very fast in teamfights (Katarina).

heroism: overheal, triumph, presence of mind

overheal: bloodthirster passive for free. Good on mf since damage to the shield doesn't count as damage dealt to her and she keeps strut. Stacks with bloodthirster and 300% effectiveness from ally shielding.

triumph: pretty much all fighters get this. Aloows you to survive ignite if you kill someone. Free 20 gold on kills.

presence: get mana when attacking champions and restore 15% max mana on champion takedown. Good if you need large amount of mana or are mana hungry (cass).

legend: alacrity, tenacity, bloodline

these are basically tertiaries and don't matter. bloodline scales harder but alacrity is better early. Tenacity if there's cc but you dont want merc treads, like vs nasus.

combat: coup de grace, take down, last stand.

these runes are pretty self explanatory, the only thing to note is that coup de grace is always 8% extra damage below 40% hp no matter how low or high their hp is. If they are at 1% hp it would be the same damage as 39% hp, while take down scales from 5% to 15%, and last stand from 5% to 11%.

Keystones: grasp, aftershock, guardian

grasp: even though it has infinite scaling with health, this rune doesn't scale all that well because melee champions can't proc it without being in a fight, and late game fights don't usually last that long since instead of one person you'll be fighting 5. Ranged champions gain 40% less use from the rune, but can use it more often. Good on gangplank, and dont use this with resist tanks.

aftershock: basically grasp for resist tanks. Very good, nearly doubles your bonus resists for 2.5 seconds after immobilizing an enemy (+80% mr and armor). Bonus resists capped at 80-150. good to survive engaging in teamfights. Nice on rammus

guardian: shield yourself and a champion for a percentage of your bonus health. You will build this solely as a support.

strength: demolish, font of life, shield bash

demolish: gain a large amount of damage on your next attack to turrets periodically based on your health. Good for taking plates if you have health tanks. Great for split pushing with sion.

font of life: good for supports, cc'ing an enemy champ causes an ally's auto to heal them. Take for support or team play.

shield bash: getting a shield gives you a small amount of mr and ad, and gives you bonus damage. good option if you have a shielder or a shield.

resistance: conditioning, second wind, bone plating

conditioning: good for any tank, gain 9 mr and armor after 12 min + 5% to each. Get if you are confident in surviving lane.

second wind: good, but better for hp tanks, as it heals 4% missing health, and only 6 health flat. great against poke lanes.

bone plating: good, great with resist tanks, as it gives flat reduction (so resists increase the effective hp it gives). no good versus poke lanes and sustained damage (quinn, singed)

vitality: overgrowth, revitalize, unflinching

overgrowth: gain hp when near minions or monsters that die. Don't get this for jungle. gain 3.5% max hp after roughly half the game.

revitalize: increased shield and healing, more effective below 40% hp. works with pretty much everything. casting and receiving (when casting takes the health of target into consideration). Decent at all stages.

unflinching: gain 10% slow resist and tenacity increased to 30% when you are at or below 30%. self-explanatory, build if they have a lot of cc or slows.

Keystone: Aery, Comet, Phase Rush

Aery: very low cooldown at close range. damages and shields. Procs on auto attacks. Good on a variety of champions (teemo, sona, soraka, yuumi)

Comet: extra burst, recommend on champions with damaging cc abilities so it can't be dodged. Dealing ability damage to champions lowers this cooldown. Deals less damage than electrocute and can miss, but can be activated with one ability and the cooldown can be lowered, plus it can hit multiple champions.

phase rush: electrocute but instead of damage it gives move speed. Good on ryze and udyr. Darius, too, in some matchups. Great for sticking, great for disengage. Also gives 75% slow resist

artefact (that's not a typo): null orb, mana flow, nimbus cloak.

these ones don't really matter. ap shield on a minute cooldown, extra mana, and speed on summoner spells. You'll usually use nimbus cloak if you get this. Mana flow if you are really mana heavy, but it only increases the maximum mana until you max it. Mana flow good with tear.

excellence: transcendence, celerity, absolute focus.

transcendence scales the best, celerity if you rely on movement or roam a lot, and focus for early game strong power (don't take into losing lanes obv).

power: scorch, river walking, gathering storm

scorch for laning, river walking for jungle, gather storm for late game.

keystones: electrocute, dark harvest, predator, hail of blades

hail of blades is a good option for assassins that use auto attacks. Possibly could use on kindred if you want to gank really fast.

electrocute: most people take this. 3 attacks or abilities give a burst of damage. Don't underestimate this, it's basically a 4th basic ability. get on people who have combos of 3 or more hits. Or you can auto weave.

predator: run people down. Use on fast people to go even faster.

Dark Harvest: basically bm. By getting this everyone on the enemy team targets you and you are telling everyone else that you are smurfing and will win lane with ease. Resets on kills so it's better for multikill assassins like khazix.

malice: cheap shot, taste of blood, sudden impact

cheap shot is good if you are cc or someone on your team has it. Taste of blood is fleet footwork but worse, good for laning. Sudden impact is for people with dashes, but mostly mid laners or bot. You don't want to take sudden impact into someone like rammus.

tracking: zombie ward, ghost poro, eyeball collection

get eyeball collection.

zombie makes enemy wards spawn ally wards on breaking, and ghost makes your wards last 60 more seconds in a weaker state. Eyeball collection gives adaptive force on kills and assists.

hunter: ravenous, ingenious, relentless, ultimate.

these are mostly self explanatory. Get relentless if you are a jungle or roaming support. Ultimate cdr is different from ability haste.