Saw this on R/LoL and found it very informative. Worth the read if you have a moment! (Credit to Elyndar)

"Hi! I'm Elyndar, and I play as Dr McB on the NA server. I'm here to show everyone a guide on how to improve at one of the fundamentals of league of legends: csing. I wrote this guide with it aimed towards bronze, silver, and gold tier players, however platinum and diamond players could learn something from following these exercises as well. I main adc and support so the guide is made bot lane focused, but other lanes could benefit as well. This is my foray into writing guides so any critiques would be welcome, but try to keep it constructive, polite, and specific please. If this post goes over well I will probably do a series on other aspects of the game and how to improve at them.
No one wants to do things for no reason, so to start with let's ask the question, "Why do we want to learn to cs?" In any game of leagues there are a few constants that do not change from game to game, one of which is minions. Let's say that I go into game and by the end of a 30 minute long game I get 150 cs. Most players think something along the lines of, "Hey, I got 150 cs that's good!" Unfortunately it isn't that good. Why do I say its not that good? To answer the question let's look at some minion math real quick shall we? Minions spawn at 1:30 and start fighting the enemy minion wave at 2:00. Minion waves spawn every 30 seconds, each wave consists of 3 melee minions, 3 caster minions, and every 3rd wave has a cannon minion added in. This means that every 1:30 there are 19 minions in total that come to lane. 30:00 minutes / (1:30 minutes / 3 minion waves) = 60 minion waves, subtract 4 waves for the first 2 minutes before minions arrive to lane and that means that in theory it is possible to kill 56 minion waves by 30 minutes. 56 minion waves * (19 cs / 3 minion waves) = ~355 minions. 150 cs / 355 cs = 42%. This means that if you get under 5 cs per minute in a 30 minute long game you are getting less than 50% of the possible gold you could have just from minions. How much gold does this add up to in game? If we assume the average minion is worth roughly 20 gold then the maximum I could have earned in the 30 minute game just from minions is 7,100 gold. Instead I earned 3,000 gold. This is a difference of 4,100 gold, or if we count it in full value kills it is almost a 14 kill difference. This means that a 5/0/0 Akali with 100 cs by 20 minutes is actually equally as fed as a 0/0/0 Graves with 175 cs, and that's only if we ignore the diminishing returns for repeated kills on the same person. With this math it is abundantly clear how much improving your csing can really change your position in the game.
Now that I've gone over some reasoning for why to learn to cs, let's go over how to actually get better at it. The only way to get better at csing is to go out there and practice. However, before you queue up thinking that you're going to magically improve leaps and bounds by reading this guide, let me tell you it's not that easy. Queuing up is one way to practice, but in my opinion it is not the most optimal way to practice. In my opinion the best way to practice something is to isolate the individual core skills and focus on each skill one at a time, then work on bringing it all together and doing it all at once. Why do I think this? Because if you try to do everything at once all the time you will water down the effects of your practice, and not get maximal results. Also in every area of life there is the ability to use a thing you are really good at as a crutch to cover things that you are bad at. In any matchmade summoner's rift game there are a million things that could distract you, but in a custom game there is a lot less there to distract you from working on your fundamentals. Therefore I have designed nine exercises to complete in a custom game during the first 5 minutes of game time. Why 5 minutes? Because it's most difficult to cs in the early game, and because the exercises are only 5 minutes long it's very easy to fit them around other things. Just slip one in every now and then while waiting for friends or whatever. Most people I tell this say, "It's boring I don't want to." or something along those lines. If you're really trying to get better and do outside reading or watch lcs games or whatever, then you can surely spend 5 minutes every once in awhile improving your fundamentals. There is no excuse to not do it if you really want to get better. All pro level players get about 10 cs / minute regularly (note this is only possible after 11 minutes in unless you farm jungle or other lanes). If they can get 10 cs / minute in pro games with their jobs on the line and you can't even manage to do it without any pressure on you, then how can you expect yourself to carry yourself very high up the ladder? Your learning will progress through a series of exercises as you get better and better. Note that the maximum possible cs at 5:00-5:30 is 38 cs. The exercises are as follows:
1.Get at least 95% of max cs with full runes and masteries, no lane opponents, and normal items. This will let you cs almost perfectly when no one is bothering you and makes it a huge problem for the enemy team to leave you alone in lane for long periods of time, as you will get farmed very quickly relative to other players.
2.Get at least 95% of max cs with full runes, masteries, no lane opponents, and normal items, but this time you must keep moving between each auto attack. Stay out of auto attack range of the minions before you last hit, and go in for the minions only when you will get the cs in one hit. Note that you can cancel the second half of the auto attack animation by clicking immediately after the damage applies to the minion for melee champions and after the projectile leaves your character for ranged champions. The reason for this exercise is that it naturally increases your mechanical ability, ability to remain mobile even while csing, and allows you to remain somewhat safe most of the time in lane.
3.Get at least 95% of max cs with full runes, masteries, no lane opponents, normal items, you must keep moving between each cs, and this time you must alternate on each wave between auto attacking as much as possible and auto attacking as little as possible. This teaches you how to both push and freeze a lane when alone thus giving you the option whether to go for turret pushing or freezing depending on the in game situation.
4.Do step 3 again, but this time with 1 bot as your opponent to simulate an enemy laner's harass. You can ensure 1 bot in your lane by adding 3 bots to the enemy team. 1 will go to each lane. Remember your goal is not to kill the bot, but to perfectly cs even while the bot is in your face. This will help you not only focus on the minion wave, but also on your laner as well.
5.Do step 4, but instead of 1 bot have 2 bots for even more harass. You do this by adding a full 5 bots to the enemy team. I'm not one hundred percent sure you can have 2 bots in mid lane as I have never really tried, so mid laners will either have to settle for 1 bot or move to another lane unfortunately.
6.Step 5, but drop your runes, masteries, and items. This makes it a little harder on you, as well as making it a little more similar to a real game in the sense that the pressure for making mistakes is higher, because the bots will pack a much larger punch if you're not running runes and masteries. It also teaches you how to cs by a smaller margin getting you out of the habit of autoing whenever the cs is just below 1 shot. It'll teach you better how to walk the razors edge between a minion having 10 hp when your auto hits and a minion having 0 hp when your auto hits.
7.Do step 6, but whenever you start an auto attack press tab and examine the enemy team, your team, what items everyone has, who is doing well, who is feeding, team comp, summoners and what cooldowns they have, etc, or look at the minimap and determine where everything is, or examine other lanes temporarily to check hp values and such. Which of these to do depends on how much time you have between when one minions dies and the next will die. This reduces your tunnel vision and promotes an understanding of the game as a whole even before grouping up, as well as teaching you to plan when to get cs and not get cs.
8.Do step 7, but keep track of both their minion wave and your minion wave. Later on this will help you to plan harass better on the enemy, so it's best to get in the habit now.
9.Do step 8, but try to make the minion deaths on both sides alternate so there is only one minion dying at any one time. This will help you get maximum harass off at a later point so again it's best to get in the habit now.
Before I end, I want to give some parting advice on things you can do to help yourself. Writing down your cs per game before and after you finish the practice can show you how much you improved over the whole regimen. You can check if you will kill a minion by left clicking them, and comparing their hp and your ad. For minions armor is negligible so you don't really have to keep track of it. For minions under tower it takes 2 turret shots and 1 auto attack to kill melee minions and 1 turret shot and 2 auto attacks to kill ranged casters. I don't know numbers for cannon minions I play it by feel, so if anyone has exact numbers feel free to shout out. You can check the turret ad if you don't know how much damage it will do. If you finish the whole thing I guarantee you will be better at csing than when you started. After you finish you should have a gold advantage in lane. The gold accrued by csing will become the foundation that you can use to improve on all the other aspects of your game. No matter what happens in game whether it is a 4v5 or whatever, there will always be cs to be gotten. Thanks for reading and I hope that this guide helps you!
TL;DR: Learn to cs properly and you will be able to carry yourself higher than you currently are."

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Also, if anyone would like a partner to go into custom games and practice with/against, I'm up for it. hit me up in game!

so many words my eyes are blood now

I didn't read the WHOLE thing as it was kinda long but this guide is good if you have the time and patience for it.

To add to the guys advice: Pick a champion that rewards you for last hitting such as Annie, Gangplank, Irelia and Cho'gath. These champions have abilites that make it easier to last hit with and reward you with something for getting the last hit on a minion such as mana returned or bonus gold.

Good luck!