I believe a lot of things factor into the determination of your rank at the end of each game such as your KDA, dmg done to champions, towers taken. But is there a specific standard you need to achieve to earn an S rank? Is there actual numbers that need to be hit?
Tyrone Lannister1 votesNot from what i can tell. I know CS is factored into it
masterdragon4811 votesI believe your performance over a number of statistics including CS, kills, deaths, assists, time dead, damage dealt, damage taken, damage to champions dealt, towers taken, inhibs taken, etc are compared to the average of all the people playing that champion. If your performance is an outlier, you will get a very high or very low grade (depending on if you completely sucked or if you did really really well).
So basically, if the average Annie player only gets 3 kills every game and you get 20, you should be well on your way to earning an S. (A horrible example but just go with it).
KVbqbFsC8e1 votesNope, there aren't any set numbers required which makes it pretty unknown. Seemingly the biggest factors are CS and deaths. Highest CS/Least deaths are usually enough for me to get an S.
Roar of Legend1 votesKill participation and death.
How fortunate that I literally just got an S- just now, so let me tell you a bit from my observation compare to the most fed person that did not get an S
Even though the Jhin have higher kill than I am, I have more kill participation and only 1 death compare to his 7. This make the kill gap of 8 vs 13 a big deal since my KDA is much better.
I do not believe that CS/gold income is a big factor to mastery ranking. I played support quite often, without any CS, gold, or damage output. I still manage to get an S many times.
Therefore, if you want an S... participate in kill as much as possible while staying alive at all point in the game.
I see 
get S quiet often. She's just so safe due to her kiting and peeling potential, while getting penta assists in every fight. Yet she hardly do any damage or get any CS.
Simple Moon1 votesFrom what I was told a while back earning an S on a champion goes like this. Say you play Ahri mid, your overall score, KDA, CS etc are calculated against everyone else who has played Ahri mid. Obviously there are different tiers. That is why a Ryze support can do almost nothing. Get normal support stats and still get an S because people don't play him often as support.
LankPants1 votesDon't miss CS and don't die. I think these are the most important factors overall.