League of Legends (LoL) Question: Cs'ing effectively

There's a few things you could do:

• First of all you should know how much damage your champion does to lane minions with 1 basic attack. This is primarily for champions that rely on auto attacks to last hit, like AD carries or melee champions.
  Let's say you deal 48 damage to a minion, now click on that minion to see it's health bar.
  Once it reaches 48 or less health you know you can last hit it.
  It isn't effective to do this all the time during a game and I am not telling you to do this 24/7.
  But it might give you an understanding of how low a minion has to be before you can last hit it.
  
• Same thing as I said before but now with ability damage. If you know how much damage your ability will do to a minion, you can effectively use it to get the last hit. This can mostly be applied on mages.
  
• Next thing you can do is play champions with strong wave clear, because they are easier to cs with. Once you understand the basics on these champions, you will automatically learn how to cs on harder champions.
  Champions with great wave clear are for example: Malzahar, Anivia, Syndra, Jinx, Caitlyn, ...
  
  But in the end if you want to learn how to cs effectively you will have to put in a lot of practice.

Alot of people try a champ 3 times, get destroyed, let that get to them and never try again.
Keep on trying, your not going to get to an okay CS number in one or even two days.
Stuff like that takes practise, even champions that are considered easy to pick up take an relative long time to master.
Find an champion your just naturally good at, if there arrent any champions you are actually good at branch out and try untill you do.

It took me 8 months to find my pefered champion (Sion) and after 3 weeks of spamming him I can say I gotten really good (for people aroud my MRR) with him, to a point were I barely miss CS and win fights I really shouldnt. (against Fiora for example)

But thats because I realized I found a champion I was above avarage with and I understand his kit from the getgo.
Your going to make insanly stupid mistakes, like I used my R to bump into walls instead of enemies, when trying to charge up my Q for a stun I actually had my back turned to the enemy at times.
Stuff like that is going to happen, its a matter of practise and howmuch you actually want it and are willing to learn/put time and efford in.

Its a useless answer but trust me when you find your champion and are able to carry games with him feels REALLY rewarding.
Dont give up though, cause there were times (and still are) were I get completly destroyed or simply dont know how the matchup will/should go.

League feels 90% fighting against tilt and disapointment from time to time and you have to be able to mentaly handle that type of disapointment. (and often hate from teammembers that comes with it)