Farming is the act of killing waves of minions and monsters to gather gold and experience. Farming is an essential component of early-game laning, when players try to overpower the enemy through an arms-race. Early game is the safest time players can farm to buy items and learn abilities that increase their power.
The minion kill count is a tracked score, commonly referred as Creep Score (CS). In the early and mid game, CS and Kill to Death Ratio (KDA) can be used to gauge a player's performance compared to their respective lane opponent.
How to Farm
Gold is granted to the champion that deals the killing blow on a minion or monster. This is known as a 'last hit' and is considered one of the most important skills in League of Legends. Many players will use their basic attack to Last Hit, but several champions, especially AP champions, also have low cost executes or area burst to last hit. Melee minions can take two tower shots and be easy to attack for most AD champions. Caster minions are best to hit once after taking a single tower shot.
When to farm
The early game, also known as the Laning phase, is the safest phase for farming, when champions are not well equipped for fights. Because of this inability, progression in the game is more focused on gaining power rather than claiming objectives. Once players attain access to all their abilities, farming becomes less of a priority as objectives start to become viable goals.
Players have adopted a number of techniques to manipulate the minion wave to their advantage.
Freezing a minion wave is often done to secure a safe location to farm, it can also act as a preparation to slow push the wave. To keep a minion wave in place, a laner essentially attempts to maintain the equilibrium of the two opposing forces. This is determined by gauging a negative correlation between the timing of the allied wave's arrival to the fight versus how many extra enemy minions are already fighting (ergo, if the allied wave will arrive sooner, more extra enemy minions are needed alive).
Freezing becomes ideal during the early game when champions are not powerful enough to claim objectives, and therefore the fight maintains within the territory limits where freezing is easier to manage.
A fast push aims to accumulate a large minion wave by allowing a given wave to push with a numbers advantage, creating immediate lane pressure ideal for quick responses. To create a fast push, a laner would remove all but the weak caster minions (they have no armor/magic resist) as an easy force for the allied wave to overtake.
Fast pushing becomes ideal when one desires to create immediate lane pressure, such as a response to enemy inattention, or to pressure the enemy out of tower defense.
A slow push accumulates a large minion wave by allowing it to push at the slowest possible rate while maintaining advantage, the resultant wave can pressure a tower and serve as a dangerous concern for the enemy. In enemy territory, the numbers advantage will have to become greater and greater to counteract the quicker timing of enemy reinforcements. To create a slow push, a laner would remove all but melee minions (they have armor/magic resist) as a formidable force for the allied wave to overtake. Seige and Super minions will need to be removed due to their sheer impact on the battle.
Slow pushing becomes ideal when a laner is required elsewhere and cannot maintain the lane pressure, such as when teams gain enough power to start focusing on kills and objectives. By leaving their wave at an advantage, it will eventually accumulate into a force that substitutes the need for a champion.
A wave in Summoner's Rift consists from six to seven minions and has value of at least 355.5. As the passive gold gain is 19 gold per 10 seconds this translates that being able to clear each minion in a wave generates roughly double the amount than simply standing around. As wave value slowly increases over time clearing out a merged wave can result in a significant burst of income.
Below there's an updated (Season 10) table chart for the perfect CS at given minutes up until an hour of gameplay. Times are for when the next wave spawns, (e.g. first wave spawns at 1:05, second wave at 1:35, meaning, up until 1:35, only 6 CS are possible). The table does not take super minions or jungle monsters into the calculations.
Super minions only spawn on lanes where enemy inhibitors are destroyed, 7 minions per wave for 5 minutes in this order: super minion, 3 melee minions and 3 casters minions. When all enemy inhibitors are destroyed, super minions are doubled on each lane until one of them respawns, creating waves of 8 minions each.