Often times it's obvious during champ selection that your team just isn't going to do so hot, and other times it seems like they won't do so well and it works out. Pay close attention to champ selection chat, be verbal, be clear, and compromise. If 2 or 3 people are bickering over the same position and not willing to do whats best for the team and work it out, then the game is probably not going to go so well. Work on being intuitive during the selection process.
It's a process a lot of the time, if things are just going horrible, pick the worst imaginable champion you can think of, don't say anything, just legitimately act like it's what you want to play. Pick Master Yi and say you're going adc, and lock it. Hopefully they'll dodge. If they don't just dodge at 1 second and take the 30 minute penalty (You can really only afford one or two dodges a day depending on your time schedule) and go play on a smurf account until your time is up. Hopefully, someone else will dodge, when they do make sure you drop yourself out of que and take a 5 minute breather to avoid being put back into champ selection with the same group. It's just one strategy to help you avoid obvious problematic teams, it's nothing to be ashamed of, it's strategic.
Secondly, even though this goes against so many peoples personalities, a lot of the times what your team needs in a rough spot is a cheerleader. Offer encouragement and sound advice in a manner that hopefully will not aggravate others. Shy away from negative criticism, shy away from criticism period (save it for after the game and then do it in a manner that's not demeaning to the other person).
Hands down, the largest barrier to overcome in winning a League of Legends match is a poor team morale. Bickering, negative attitudes, insults, arguing, these are all contributing factors that can and will make you lose often.
Learn all the roles, and learn multiple champions in each role. Become proficient with them, learn your counters for each champ, and learn what champs you can counter with them. Learn the strengths of each champ and what champs they work well with on a team. If you have Malphite top, and decide to teemo mid, that will not have the same synergy such as Zyra + Malphite, or Amumu + Malphite.
Lastly, set goals, but set them small. When you reach that goal, set another. Towers aren't built with one long piece of metal, there's many different sections that need to be laid, from the bottom up before you can reach the top. If you have a bad game, or just can't avoid a bad team, or even have a bad streak, don't worry just shrug it off. Very rarely will you have a constant pattern of win-win-loss or loss-win-loss-win. Wins and losses will come in streaks.
Anyways, hope this advice was helpful. Sorry for the novel.