I used to tilt very frequently as well, and what helped me the most is taking a very, very long break from League of Legends. I stopped playing for a good six months to get my head on straight. I needed to refresh my perspective on league - I needed to make the issues I faced in there so much smaller than what I experienced every day. When you take the game as just a game, it's a lot harder to get mad at it, because it means a lot less to you as "just a game." But if you see the game as a way to win, or a way to get LP, or the way to get respected in a community, then the game means way more to you, so you get angrier at it.
The healthiest way to see the game as a game is to see it as self-improvement. You're improving your mechanical skills at a game, or you're improving your sense of the game, or you're improving your shotcalling ability - hell, even improving your attitude and communication - anything, as long as you see it as the improvement of a skill, will keep you from tilting. Even losing in that mindset won't tilt you, because you can still improve, and still learn as a result of a loss, just as much or even more than a win.
The attitude change also prevents other people from tilting you. That's because when you improve yourself, you're the master of your domain - you're the only one who can make yourself better after all. Even coaches, who will tell you what to do, aren't the secret to improvement - the secret to improvement is to adopt better and better ideas and implement them over time. The only thing a coach does is introduce you to better ideas earlier; you still have to implement them correctly. When the other person on your team is telling you "you suck yo" or "go die in a hole" or anything like that, it's easy to block them out as long as you focus on yourself, and your own improvement.
Hell, you won't even have time to respond. That's how focused you should be. Granted, still take your team comp, team cooldowns, enemy cooldowns, etc. into account, but what they're saying doesn't matter, because what they're saying won't help you improve. Unless they gave you an enemy flash timer (or something related, like an ult timer), or a strat like "let's bait baron," pay them NO mind. They won't help you. Only YOU can help you.
Another good option is just /muteall, if you know things will be bad from the get-go. Turning down ping volume will help a lot, if players are using pings to tilt you.
My final tip is to find a group of friends that will NOT take your bullshit. Queue up with them, and tell them that they have full rights to police you when you're being an ass. And LISTEN to them. If they say "stop typing and play," go against your gut instinct and LISTEN. It will eventually become a habit. Hell, even playing ranked with friends over Skype will help you, as you don't pay as much attention to chat in those situations.
Anyway. Focus on yourself. And no one else. Only then will you improve, and see results. In all aspects of your play.
