Credit to Bartalon for this picture.
Having a lot of gold in the mid game increases your chances of out damaging your opponent and more likely to win team fights. This is blatant and anyone could tell you this, but what is the most effective and fastest way to generate gold during the early to mid game? The most obvious way is getting kills, of course, getting one normally yields varying amounts of hundreds of gold just in a matter of seconds. However, despite this, it should not be your main focus for generating gold for several reasons.
The main reason why actively going for kills to gain a gold lead is because there are creeps that spawn every 30 seconds for you to farm to your heart's content. This can't be right though? Creeps give significantly less gold for each one than a champion kill so it would make sense to make champions a higher priority. Well, while the amount of gold per champion kill is significantly higher than a single creep, the numbers do not lie and creeps are more important to pay attention to.
Every 30 seconds a new wave of creeps will spawn starting at the 1:30 minute mark, basic knowledge, but there's more to it. Every wave will have 6 or 7 creeps. The wave with the 7th creep will have a cannon minion in which has significantly more gold. The waves go as such 6-6-7 and the cycle repeats. It is important to keep track of when the cannon creep wave is on its way because it can push a lane and also means that you do not want to miss out on killing their cannon minion.
Here are some statistics that most people never see or think about Theoretically, with a perfect creep score, at around 5:30 on the timer, it will be possible to have 50 creep score which is 1008 gold. If you did not buy any starting items (just as an example) the 475 gold at you receive at the beginning of the game plus the 748 passive gold and the 1008 gold from creeps, makes it possible to have a total of 1756 gold, which is enough for a bf sword at the 5:30 mark. Most people are not even able to purchase a bf sword until 10 minutes into the game which makes that bf sword at 5:30 a big advantage. The gold generated from the creeps at the 5:30 mark is about just as much as 3 champion kills, an extremely difficult feat to pull off so early in the game. Creeps will always have the same prioritization and AI while players will always have different play styles and skill levels, making creeps the most consistent way to generate gold. Another way to look at the importance of getting the best creep score possible during the early game is looking at the gold per 3 waves. The amount of gold that creeps reward consistently increase as the time in the game ticks on while the amount of gold players are worth fluctuate based upon their kills and deaths. Even for the very first 3 creeps waves, the amount of possible gold earned from the first 19 creeps is 381. That equals more than a champion kill every minute and a half. Suggesting perfect creep score, at the 10 minute mark, 18 waves will have spawned which amasses to 114 creep score. A creep score of 114 is about equivalent to 7 kills.
However, having a creep score of 114 at 10 minutes is under perfect conditions, is nearly impossible during an actual game (unless farming the jungle) for a few reasons. One is that you are going up against an opponent and they are doing everything in their power to farm and kill you as well, making creep scoring dangerous, even more so with their jungler looking to kill you. There also is a reasonable expectation that at some point in the game you will have to go back to base in order to heal up and buy. This means that inevitably, you will miss out on some creep score. What you can do though is minimize the amount of creeps you will miss by pushing out the lane when you are going back to base and not letting the enemy wave get to your tower. There will also be times where you will need to stop farming and go for objectives with your team and group up which will lead to less creep score which is okay since objectives are still a key part of the game. This is why farming effectively during the early part of the game is important because it is the best time to farm.
The order in which you kill creeps is also significant. Ignoring super minions, the cannon minions give the most gold out of any minion so it's important not to miss them. The melee creep gives the second most while the caster minions give the least. While creep scoring, the main priority for last hitting should be Cannon>Melee>Caster minions. If a caster and melee creep are going to die at the same time, last hit the melee since it will be more gold efficient. It is also important to note that since caster minions are ranged, that it means that you have to get further away from safety to last hit them while melee minions are closer. Under tower, melee creeps take two turret shots and one auto attack to last hit from full health while caster minions take 1 tower shot and two auto attacks to last hit. Last hitting a cannon creep under tower can be a bit of a challenge since they take too many turret shots to count appropriately and normally have sustained some damage before getting to the tower which means that last hitting it will have to be instinct and looking at how much health it has left.
Finally, the last main part about creep scoring is knowing your champion and the matchup against your lane opponent. Some matchups will mean that you will have to play careful and will result in missed creeps. An example of such a matchup would be a Heimerdinger vs. Fizz. Fizz is melee and needs to get up close to farm while Heimerdinger can sit back and have his turrets farm and poke for him which makes it dangerous for Fizz to go and farm since it will result in a lot of unnecessary damage which is not worth a single creep. I cannot stress it enough to know your champion and their matchups and also becoming familiar with their auto attacking animation along with their damage as to not miss any last hits. Even if your champion counters your opponent, it does not mean you should be constantly trying to kill them because it will lead to missed creeps and lead to being ganked. The only time you should go for a kill is if they are low, you know where their jungler and your jungler is, they make a mistake, or if you have an escape plan.
Knowing how to play safe and zoning the enemy laner while maintaining a healthy farm is what will give you the ability to gain a lot of gold and also put your opponent behind and put you into position to carry your team for the win.