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.
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. Last hitting will increase a champion's 'creep score' (CS), which represents the champion's total farm. In the early and mid game, CS and Kill to Death Ratio (KDA) can be used to a gauge a player is doing compared to their respective lane opponent. Many players will use their basic attack to Last Hit, but several champions, especially AP champs, 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 slow push will accumulate a bigger minion wave, which can pressure a tower and serve as a distraction for the enemy. A minion wave will naturally push towards a direction if it overwhelms the opposing wave, increasing in total size with each victory. In enemy territory, the numbers advantage will have to be even greater to counteract the quick timing of enemy reinforcements. To create a slow push, a laner would allow a generous minion advantage to their wave. It is recommended to remove only caster minions because they have no resistances to stall the push.
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 formidable push that substitutes the need for a champion.
A fast push accumulates a minion advantage very fast, creating immediate lane pressure ideal for quick responses. It differs from a slow push in that one would remove only melee and siege minions from the enemy wave.
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 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 8) 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.