It's an incredibly tricky technique. I've only done it once, myself.
Your choice of champion is highly important. Make the wrong choice, and you'll never do it. The champion itself must be tilting to play against, or you'll never manage to tilt the opponent near enough. Teemo is the iconic example, but you could pull it off with others. The less viable they're considered to be, the easier this is, as well.
Mastery 4 or 7 on your champion are a must. Neither 5 nor 6 will suffice.
Part of their team must be easily tillable. Someone besides who you're laning against.
And part of their team must be at least somewhat toxic to begin with. For, if they're not toxic, you have nothing to catalyze to ultimate toxicity.
You want to begin by invading. Possibly double invading. Stealing one buff? Recoverable. Stealing both buffs? You've screwed their jungler over big time, resulting in them coming in already pissed. Bonus points if you kill the ADC, support, or mid during it.
You must then immediately find their weakest link. Whoever's on the longest losing streak, whoever's already died, and whoever just seems the second most toxic. In that order, are your choices. Remember, you want the toxic one to flame them, because it'll set off the chain reaction. Then you camp them. No matter who you are. You keep going to their lane, and killing them. Don't let your team and jungle/lane suffer for this, but just keep hitting them whenever you can. The more you do it, it becomes easier twice over. Once because you're getting fed off of them, putting them behind. Second, because they're going to play dumber and dumber.
Keep doing this, and let the toxic player flame them. They'll start flaming, too. And if there's just the right elements on the opposing team..