Okay, here we go.
So you have plenty of champions; each week you get 7/10 Free Champion Rotation. New members get 10 champions instead of 7 (I think) during the first couple of weeks or something. What's important at this stage, is that you play each champion you haven't played before in each rotation, at least once. You'll learn a lot about a champion just from one game, you'll learn his abilities and how much damage he can do, It'll help you when you go against that champion in other games.
Your build is important, depending on your role, you customize your items build to counter your opponent's strength. For instance, if the enemy team has a lot of AD champions (Attack damage) then you build armor to counter that - if you're a tank. However, if you're a tank and you build damage instead of armor then you'll die easily in team fights and won't be able to fullfill your duties and tank damage for your squishy team mates. That's just one role.
There is many different roles in LoL:
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Tank(Top lane/Jungle): Tanks go Top lane or in the Jungle most of the time. They build Armor and Magic Resist,one more of the other if the enemy has unbalanced team: You build Armor depending on the enemy's AD and you build Magic Resist depending on the enemy's AP (Ability Power). AP's are mages meaning they do damage with their abilities mostly and not with their AA (Auto Attack). If you're a head, 2 items should give you enough time in team fights to tank damage and get out before you die. However, you can always decide to go suicidal and tank more damage and die if it means your team can win the team fight, and then the game.
-Jungle/Jungler: A Jungler role is the most important role in the game, nobody could argue with that. A Jungler role is to clear jungle camps and gank lanes. Each Jungle champion has a unique character. Some are early-game junglers, some are late-game junglers. With early-game junglers you seek to gank lanes before the 20 minute mark otherwise your champion will start doing less damage and turn into more of an utility champion. With late-game champions you get a weak early-game damage and ganking ability so you keep farming your jungle until 20 minute mark, then you start ganking. It doesn't matter which champion you're on as long as you know what lanes needs t be ganked, and more importantly, when to gank. I wouldn't recommend playing this role until you're at least level 15.
-Middle Laner(Mage/Assassin/Fighter): As a middle laner you have the burst damage to take someone out with one combo, or poke someone to death and force them back to their base and have either a 5v4 team fight or a free objective since you'll out-number your enemy's champions. As a middle laner, whether you're on a mage champion, an assassin, or a fighter, it's important to know when to engage. Most middle lane players tends to be hot-blooded and jump in first during a team fight before the tank could position himself and get themselves killed, and then lose the team fight. You need to make sure you're not being focused, you go in after your tank, or if you're fed then you make it quick: kill their squishy carry and back away quickly.
ADC(bot lane): ADC refers for Attack Damage Carry. Being an ADC is extremely important mid to late game - since you do no damage early game. ADC can carry an entire game if they're fed, so make sure you always have your ADC protected if you're a tank or a support. Being an ADC meaning you go in LAST during a team fight, you cannot get yourself focused by the enemy's carries otherwise you're pretty much dead. You attack whoever is in your range and kite them back and forth by taking no damage if possible. Also, don't hesitate to jump in a fight if you know your team got your back, just make sure no one can burst you with one combo.
Support(bot lane): Support is a tricky role. You don't get to do damage but it's hard to stop yourself from attempting to, eventually you get yourself killed and lose the game lol. I main support myself so i know that for a fact. Being a support meaning you'll 'carry' your ADC until he's strong enough to stand on his own and start doing damage, being paired up with a 'bad' ADC will hold you down, if so, just build damage and go
#YOLO. You job is to peal for your carries, sometimes it's not the ADC, it could be any other champion on your game: Top laner, Jungler, or Middle laner. Most of the times it's your middle lane to be honest. However, that doesn't mean you just leave your ADC, nah, you stick with that dude as if the two of your are married and hate each other, but you're still married lol. You customize your build depending on which support champion you're using, some support champions build a little bit of damage while focusing on utility items as well; some get tank items while still getting the utility items; some only get utility items, it's your pick. Support isn't an easy role, and it's not a 'cool' role where you get to kill people. Your job is to make sure your team mates live as long as possible during a team fight, peal for them. As a support, you make sure to use your abilities to set up kills, you probably on a champion that have tons of CC and pealing ability, so don't shy out and run from a fight if someone else on your team is still fighting.
Champions that are viable in each role/lane:Top lane: Mundo(Tank), Rumble(AP), Lissandra(AP), Kassadin(AP), Riven(AD), Maokai(AP/Tank), Irelia(AD/Tank), Darius(AD), Renekton(AD/Tank), Kayle(AP), and a few others.
Mid Lane: Orianna(AP), Zed(AD), LeBlank(AP), Syndra(AP), Jayce(AD), Twisted Fate(AP), Lulu(AP), Karma(AP), Talon(AD), Azir(AP), Yasuo(AD), Lissandra(AP), Kassadin(AP), and a few others.
Jungle: Rengar(AD/Tank), Vi(AD/Tank), Nocturn(AD), Jarvan V(AD/Tank), Fiddlesticks(AP), Amumu(AP/Tank), Lee Sin(AD/Tank), Kha Zix(AD), Shaco(AD/AP), and a few others.
ADC: Corki, Lucian, Jinx, Draven, Sivir, Graves, Tristana, anything works if you got the items.
Support: Thresh(Tank), Braum(Tank), Leona(Tank), Karma(AP), Morgana(AP), Janna(Tank/utility), Nami(Tank/utility). Supports doesn't build 'Tank' or 'AP' items, those just come in handy in some combos. You always focus utility.
Positioning: In a team fight it's important that you position yourself correctly, if you're squishy then don't go anywhere near the front lines. If you're a tank make sure you're always in front of everyone else. If you're a support make sure you're always close to everyone on your team who's engaging the enemy team champions, or going to. If you're ADC then make sure you AA always when you're close enough but don't hesitate to flash out if you get focused. If you're on a bursty champion, you could always dive in and try to get kills, but stay close to your tank and support.
I think that's all ._.