To "carry" games in short you must have great objective control, map awareness and team fight presence while being the one on your team who is doing the majority of the "heavy" work. Killing is often associated with that. Being a carry for the game especially in solo queue often times requires you to be a shot caller so that your team can be in the right place at the right time doing things to make the most of your power during that stage of the game.
Often when I carry I ping a lot and direct where to go next. If my team is mostly in another lane and are at a stale mate with the enemy, I tend to split push to divert them to my lane. Being the carry and winning games is all about making the right moves in the situation. You wont make the right move all the time but the more often you get into the situation to CONTROL the game with your presence, the more experienced you will become at it.
I honestly recommend watching some Vod's of some LCS or Worlds s4 play. You can pick up a lot of good habits and basic objective control strategies and scenarios. Just remember one thing, if you see that you are carrying a game and you are in the lead, DO NOT THROW. If you feel your team is a little lost on what to do next, take control (politely but firmly) and make sure you capitalize on your lead. Too many times in lower elo will players in a lead get lax and let the game run on for waaay too long.
Before you know it you have a ton of kills, ton of assists, not many deaths (or many) and yet you still lose. The game is still a team effort no matter how well you do individually, you need the other members to at least play well enough to not throw away their leads. Otherwise, for every mistake they make, your tasked with cleaning up, and sometimes thats too tall an order.