Here are my tips to climb easily.
- Start with muting everyone in the game to help you focus and not tilt at all, this way you wont challenge yourself to type or encourage typing from others when typing to them.
- Play cheesy champions (veigar is good), by what I see from your match history you got really good scores on him, but like everyone, farm can get better, so make sure you pay attention to farming well.
- Once you get ahead you should also try roaming (I think roaming to bot lane is the best since it can tilt 2 players at once, but you can still do it to top lane too of course) to other lanes and put deep wards in the enemy jungle, so if someone is low or not paying attention, Im pretty sure you could secure a kill on them (also without them being low since you're playing Veigar)
- Push, push, push, push, push. Focus on objectives rather than kills, now Im not saying dont get a possible kill if you can, just to deal some damage to turrets, but always push lanes, and after a team fight try to get a turret or two if possible (do it safely and notice the enemy death timers, so they wont catch you over-staying). a dragon is also good.
- Play the nasty side of the game. Tilting the enemy team already in the early game is what will win you the game probably, because in low elo players find little to no interest in playing matches in which they fall behind in the early stages of the game. Picking a snowballing lane bully/champion with really strong early-mid game should do the job.
- Find good players around you, and try to duo/trio with them. If you can communicate with them through skype or teamspeak all the more it benefits you.
Other than that I think champion experience is one of the most important things in the game, dont go into an uncomfortable pick because in low elo team compositions rarely matter. Pick your best champions in every role and be sure to play them as much as possible, so you'll have the upper hand on the enemies already since the beginning of the game.
Except that, there are plenty of micro plays (trading, warding, itemization, champion/matchup knowledge) that you should work on if you want to climb really easily, but after all what Ive said I cant really think of anything else that I could tell you, without further looking into how you play/communicating with you.
Good luck and feel free to ask anymore questions!