The LoL metagame:
The current standard team composition is generally an ADC (ranged physical carry) in the bottom lane with a support champion. It's the ADC's job to farm as much CS (creep score, or minions) as possible and not die. You don't have to kill champions, just outfarm them and live. The support's job is to keep the carry alive and sustained in the lane so they can continue to farm.
Ussually an APC (caster) goes middle lane, and a tanky champion with high sustain goes top, along with another tanky champion in the jungle. The early game revolves a lot around the jungler, whos primary job is actually to roam the lanes and look to gang up 1v2 or 2v3 on the other lanes. Sometimes, especially either mid lane or when there is no jungler, the lanes will roam also. It's important to have map awareness and notice when a lane goes MIA (missing in action), and run back and assume they are going to gank your lane.
In the case of junglers since they have no lane they are normally at and could be anywhere, it's important to continually buy sight wards and place them in the river on the path to your lane, and constantly look at the minimap to make use of these wards.
When the enemy leaves your lane, or goes back to base, or dies, its important to call MIA on them so your team knows they could be anywhere on the map. Always keep an eye on the other lanes and read the chat for MIAs. Sometimes people will also say SS, which means missing, or the same thing as MIA.
It's also important to keep your tower alive. If you have to go back and buy something, don't do it at a time where your tower is vulnerable. Once the tower dies, it becomes very difficult to safely farm from that lane. If another lane is not present and their tower needs defending, you should temporarily go to that lane and defend the tower if possible.
You shouldn't go back to buy items more than necessary as you lose out on farm. You should only go back when it's no longer safe to farm in the lane, or if another lane needs help. Such as when you have low health and can't effectively farm, or the minion wave is too pushed to farm without overextending, ie going too far from the tower. This is the best time to go back. Always make sure to buy atleast 1 ward and 1 health potion for safety and sustainability. A vital part of farming safely aside from warding and map awareness, is "last-hitting". This is the easiest way to prevent pushing the lane too far from your tower, where you become overextended. You always want to avoid overextending. Last hitting means instead of constantly autoattacking and using skills on the minions, you let your own minions weaken them and only attack them once for the final killing blow. This way you get maximum gold without pushing the wave too fast. If the enemy is continually pushing the wave, you want to damage the minions a little faster to make up for this, so your tower doesn't die. If they continue overextending ask for a gank from your jungler or mid lane.
For items, Boots and 3 health potions are standard for ADCs because they give you sustain aswell as being able to escape jungler ganks faster. If there is no enemy jungler, you can start Doran's Blade instead because the lifesteal will sometimes give you more sustain.
Aside from that there are 3 main stats an ADC needs to focus on: Attack Damage, Attack Speed, and Critical Chance. In general you want to first build a major AD item, then start increasing Attack Speed and critical chance. Such as getting Infinity Edge with the Critical component last, then getting Berserker's Greaves and a Phantom Dancer starting with the Zeal component. If you are having trouble being sustained in teamfights, Bloodthirster is a good alternative. If you are being CC'd (crowd control effects like stun, slow, blind, etc) and bursted (ie enemy casters using their skill combos to nuke/assassinate you) then Banshee's Veil is a good item also, or even Mercury Treads instead of Berserker's Greaves. You don't need Armor Penetration items unless the enemy has a very tank team that is building excessive armor (ie stacking armor). Then Black Cleaver can replace your first big AD item (Infinity/Bloodthirster) or you can get a Last Whisper later after your first major AD item.
Sometimes an early Phantom Dancer starting with Zeal can help you kite better in teamfights due to the movement speed. Kiting means hit and move tactics basically, instead of standing still and autoattacking a tanky champion who may have less damage but can likely kill you quickly because ADCs are very squishy champions. Instead of fighting 1v1 you want to stay near the back of teamfights and be positioned well where you can't be focused by the enemy team. Kiting and have good position are very important for ADCs.
Early game is about the laning phase whereas midgame begins when teams start moving together. Now instead of preparing for midgame by focusing on getting farm, teams are fighting over objectives like buffs, Dragon, and towers. It's important to be safe and support your team and help keep the group together, the map warded, etc because people are idiots. You do not want to get caught 1v3, 2v4, 3v5 etc or your teammates. Communication is very important now.
2 things that are important is that your support not take CS from the ADC, as the ADC is supposed to take all or as much of the farm in the lane as possible, because ADCs are the main source of damage in teamfights. If your support is taking CS, or pushing the lane by autoattacking minions, or being too aggressive when you are trying to farm, make sure to communicate and politely ask them to stop the behavior. If another lane keeps dying or "feeding", politely ask them to play passively and farm instead of dueling that champion over and over, causing them to be more and more fed. If they continue getting ganked, ask them to ward and not overextend. Or just ask them to be careful, not push lane, etc. Avoid using the word "stop" because it makes people go flip the **** out and do worse. Something like "so and so plz be care your lane is being camped" or "plz farm and not duel, k?" etc.
If someone keeps not grouping and continues simply farming and overextending, or roaming alone, overextending etc in midgame, you have to get that person to group up any way you can.




So basically the objectives are to farm, not die, and support your team, and get your team to do the same ideally.
Practice last hitting, positioning, warding, and map awareness. These are the main keys to playing well.