"Runes" and "masteries" are things that will help you be stronger through out the game. How to customizes your "runes" and "masteries" to suit your champion/role?
Being able to set up your "runes" and "masteries" will be very beneficial to helping you win games, knowing that your opponent will be able to do the same so in the end it will even things out. Every level your account gets you unlock a "mastery" point and one new "rune" slot, once your account is level 30 you will have unlocked all masteries points and runes slots. The only way to get runes is to purchase them with your "IP" (influence points), and you need to earn your "IP" by playing the game, you get more "IP" for winning games.
Level 30 is the maximum level you can achieve on your league of legends account, at this point you will be able to put 30 skill points in your masteries. To find were to customizes your masteries open up league of legends, then click view/edit summoners profile at the top right, then click masteries, at this point you will be able to customizes your masteries. You can have as many pages as you please, and name the page something what will help you pick the right one in champion selection. Example name your masterie page after a role or a champion, Top ad, Mid ap, adc, jungle ad, support, or name it the champions name.
There are four kinds of runes slots, there are nine "Marks" the red ones, nine "Seals" the yellow ones, nine "Glyphs" the blue ones and three "Quintessences" the big purple ones. All of these kinds of rune slot have style of rune that makes the slot most effective. Examples the "Marks" rune slot in best used for physical damage, like attack speed, attack damage, magic penetration. The "Seals" rune slots are most effective with defense, examples armor, health, heath regeneration. The "Glyphs" rune slots are most effective with magic, examples magic resist, ability power, mana regeneration. The "Quintessences" rune slots are effective with any type of style of rune but it also as a unique style called utility and it offers unique runes like, "life steal", "spellvamp",+1gold/10 seconds.
If you are not sure how you want to set up your rune pages or your masteries pages then look up recommendations, i recommend to wait till your account is level 20 before buying runes. Because if you buy early then that you will receive a cheaper rune that the states will not be as useful later down the line and you may have to buy it again just to get the better version of that rune. Every level up on your account you should put a point in your mastery pages, at level 21 you will be able to unlock a final tier mastery point just make sure you put all of your points in the same mastery tree. There are three different masterie trees and they are "Ferocity", "Cunning" and "Resolve" and in each one they have three choices of the final tier point but you can only pick one.
Note: Every season "riot games" changes the masteries, they may take out some masterys or add new ones or do both. A good website to help you build your masteries and runes www.mobafire.com, this website also shows you what items you should buy and where to put your level up point in game.