What roles do you play? As general advice, prioritize staying alive, focus on objectives, and keep up on farm throughout the game. Warding often and wisely helps a lot on the first two parts, practice helps on the third. Keep a positive attitude, be friendly and encouraging to allies and opponents, and try not to stress out. At the end of the day, League is a game, and if you let yourself get stressed out about it you will not have fun and you will not do well.
I would also seriously encourage you to deepen your champion pool in all roles. Even if you do not wind up playing those champs in ranked, having knowledge of those champions, their strategies, and their match-ups will make you a better and more successful player, especially if you make a point to learn niches you have never touched before. Being knowledgeable and well-rounded is no substitute for mechanical skill, but it sure is a good supplement for it.