One of the things I've tried to learn is how to synergize a team. Any time you're not a top pick, take a look at what the rest of your team has (or ask what they're intending to play), and try to find something that helps them do what those champs want to do. Oftentimes I've found that being able to make my teammates better at what they want to do goes a long way towards winning games.
For example, if your mid picked Yasuo, grab a champ with some displacement/knockup (such as
, etc) to set up his ult.
Or, if you've got very AoE focused damage-dealers (say
mid and
adc), grab someone that can keep the enemy team around so that damage hits (
, etc).
Beyond that, I think Icestar1186 covered things pretty well - and if you have to start somewhere, start with his advice before bothering with the above. First and foremost, you want to work on getting better at doing the things you need to do.
For builds - look some up, then take them to normals to try them out. Then experiment - shift things to find what works for you, then practice with that some. Be willing, in any game, to modify your build to fit the situation. Whenever you're not playing a major damage source, be willing to build for the team rather than just yourself. If no one else is building that Frozen Heart or Locket that could make the difference in close fights, you do it.
Last thing? Try to expand your playable champion pool. I like most of your picks (except Vayne - but that's just because Vayne irritates me), but more comfortable options is always good.