People are going to be dicks sometimes. Usually they start out with some minor toxic remarks, like a sarcastic "nice dive noob" when a tower dive goes bad; that is the the point you want to mute an individual, before they escalate to insulting your rank and intelligence. I don't recommend using /mute all at the start because it cuts off all the positive and useful communication, but if the slightest remarks tilt you then it's ok to do that. You might also simply move the chat box off your screen, or edit its size in the config folder so it's invisible (-150 will do).
Just remember that they are nobody important to you. They don't really know you so there's no need to take their words personally. If they are saying they'll report you and are asking for the others to do it to, you don't need to defend yourself; False reports get thrown out, and they'll have no effect on you if you've done nothing wrong no matter how many of them there are.
When someone starts flaming you, they typically want to know that their words affected you. The only way they know this worked is when you respond. The obvious solution is to not respond to them. You can certainly come back with a positive response and try to get the focus back on the game (I prefer this as the initial response to toxicity), but if they continue their behavior then it is a bad idea to speak to them any further. It's like feeding the bears; once you give them some they're going to come back for more, and you've either encouraged the behavior or made it worse.
If you ever get distraught over their behavior before you're able to block them out or de-escalate the issue, take a break from the game. If you go right into another game in that state you are likely to not play at your best and be more susceptible to toxicity. You can move from Ranked to Normals or ARAM, or log out of LoL and do something else for the time being. I suggest a nice comedy show to lift your spirits :3
Don't forget that you can always improve your own gameplay as well. While someone may have been wrong to insult you for a mistake, that doesn't mean you can't learn from it! After things go back, analyze what you did and consider what you could've done better. Read guides and watch pros/coaches to get better; if you improve you'll climb, and if you climb you'll have a much better time! (people that lose tend to be the toxic ones after all)
