In certain lanes, counter picking is essential, whereas in other lanes it’s perhaps not so important. Certain champions need to be counter picked, when other champions should only be picked as a counter pick. Needless to say, counter picking affects all positions.

Possibly the most essential place to counter pick your opponent is the middle lane. The champions typically picked for middle lane are AP Carries, and rely on their abilities for the vast majority of their damage, trading and duelling. As a result, if your opponent’s abilities counteract, benefit from or block/dodge your own abilities, then you have been countered and will find it very difficult to win your lane.

For example: Katarina vs Lux. All of Lux’s abilities are skill-shots designed to work at range. Katarina has incredibly high mobility and massive damage at close range. If Lux fires off a Light Binding, the Katarina can Shunpo away from it, effectively nullifying Lux’s combo. However, if Katarina manages to Shunpo onto Lux, Lux has no was of escaping or stopping Katarina's deadly combo. Lux can try to snare or slow her, but that won’t stop her ultimate. Katarina doesn't move when using Death Lotus anyway. Lux can shield a small amount, but Katarina’s burst will smash straight through it. Same goes for Orianna against Katarina, once her ball is out of position, Katarina has free hits in close range.

Can't do anything ;-;

Similarly, Diana counters Katarina. If Katarina jumps onto Diana, Diana will just shield herself (also damaging Katarina at close range) with Pale Cascade and if Katarina starts her ultimate, Diana can just cast Moonfall to knock her out of it. If Katarina attempts to disengage using Shunpo or Flash, Diana can chase her with Crescent Strike/Lunar Rush combo, nullifying both a Shunpo and a Flash.

Generally it’s a bad idea to pick easily countered mid champions in the first 2 or 3 picks. The mid champion should be picked either last or second to last.

The next important place to pick a counter is top lane. Again it’s a one on one situation, and again abilities can make all the difference. Cho’Gath vs Warwick is a good example. Cho’Gath’s main gimmick is his Feast, and the resulting Feast stacks. At max level Cho’Gath’s Feast stacks can add nearly 1000 extra health, without bringing items into the equation. Warwick’s Hungering Strike increases in power based on a proportion of the maximum health of his target, so you can see how this counters Cho’Gath.

Next is the jungle. In certain situations bottom lane can be more important, but we’ll come to that in a second. In the jungle you have to worry about counter-jungling, enemy ganks and your own ganks. Take Rammus as an example. He’s not a particularly fast jungler and relies heavily on being able to gank, and while ganking he relies significantly on damage from his team-mates in the lane. As a result, he is incredibly vulnerable to counter-jungling. If an enemy jungler like Shyvana or Lee Sin who can clear a jungle camp stupidly fast then high-tail it out of there, there is nothing Rammus can do about it. Even if he does catch them, he can’t kill them. He can keep them there for a while with his cc, but once his taunt is over the enemy jungler will either leave or kill him.

Then we come to bottom lane. There are counters between AD Carries, and between Supports, and between Support and AD Carries. To counter a Blitzcrank, pick Alistar. Every Rocket Grab that hits Alistar is basically a free engage for Alistar and his team-mate. To counter Caitlyn, pick Sivir and turn those Yordle Snap Traps into free mana farms with your shield. To counter Vayne, pick Ashe. Every time she rolls towards you punish her with a Volley, and when she uses her ultimate, stun her and wait it out. If they pick Ezreal, pick Taric. Ezreal relies on his poke damage to outdo his opponent. Between Taric’s shatter and heal he can nearly negate Ezreal’s poke effect. Then if Ezreal Shifts into range, Taric can Dazzle him and the friendly AD Carry can escape. If they pick Soraka, or Taric, pick Tristana. With her healing de-buff she can nicely counter the high-cooldown heals from these Supports.

Ezreal counters powerful skillshots pretty well. secondflashopbetternerf.

Then there are the overall counters. Soraka’s ultimate counters Karthus’ ultimate. Blitzcrank can keep tabs on Katarina’s mobility. Alistar can reduce Nunu’s ultimate to a slight snow-dusting with proper timing. Maokai’s AOE damage reducing ultimate can actually take advantage of Amumu’s ultimateby throwing it down inside the area, basically reducing or eliminating the advantage of keeping a team from moving.

So, in summary, good countering can give you a massive advantage before the game even starts. Many of the professional gamers in League of Legends state that winning a game starts with the first ban. At the very least, you shouldn’t make a final decision who you’re going to play until after the final ban has been made (but you should have some idea, that way you can make some really useful bans, e.g. ban Soraka if you want to play Karthus).

An excellent place to find and discuss counters and team compositions is championselect.net. You can search strong and weak versus champion picks and they've got a neat little app to help analyse your team's strengths and weaknesses.