Well, it honestly depends on how long you've been playing the game as well. A lot of these people who flame you have probably been playing the game for a minimum of 3 years, so they're not used to seeing new comers.
The only way to really improve your mechanics on a champion, is to play that champion A LOT. I'd start with something simple, for top, start off with garen/kayle/malphite, for jungle, play something like yi/warwick/tryndamere, for mid play someone like kat/annie/lux/vlad, for adc play ashe(she's really strong right now)/caitlyn/jinx and you can really pick any support.
Taken into account, a lot of this just depends on your playstyle, if you're super aggressive or incredibly passive. But one thing to keep in mind, and this helps me win a lot more games in ranked then I should, is to sustain in laning phase. Just cs until you can't anymore. If you can hit somewhere around 160 cs within 20 minutes, then go do something. People won't flame you for farming and playing passive, at least they shouldn't because, well, you're not feeding. Also, if they are giving you a hard time, just mute them. The amount of times a toxic player has carried me is gigantic, so it's better not to piss them off more or make them tilt more.