Okay, so i play almost only solo ranked, and have - as you all - been with some 4-man premades. I have tried to make the best of the situation, and have won all games with 4-man so far. The way i approach the games are as following (i play mid):
1. Play a champ you are really comfortable with. It is best if it is one who scales well into the lategame, but also is useful earlier (think Orianna or for me, Xerath). Also, i would not recommend to pick an engager, as the premade won't always follow your calls
2. Just farm and stay very safe in lane. Their jungler will camp you very quick if you go ANY aggressive, and odds are your jungler will be slower to come. Don't go for the solo-kills, as if you fail (even if it was to a gank), the premade will get frustrated if you are the only guy feeding/doing bad. So stay safe!
3. Watch the map closely. You will often be able to see when a fight is about to break out. You can count on 4 from each team being there - if you are the 5th man on your team, you can win the 4v5 easily.
4. Ping a lot, especially "missing". If just 1 from the premade sees this, he will warn the others and you can see the reaction from the rest of your team. They especially listen to you if you have "proven yourself" by being in fights and playing them well.
Finally, Riot has admitted that while the toxicity of duos and trios is lower than solo players (and most ppl seem to not have THAT much against duos or trios), the toxicity of 4-mans are higher than of solo players. If they do bad, lose botlane, and then lose a teamfight, they are gonna blame it on you - you maybe arrived 1 second late or missed a Q, or something like that. Just mute the bastards, report, and move on.