Winning ranked games
The first and most important thing you can do to raise your elo is to make sure your mindset is to win no matter what. There are trolls, noobs, and insanely stupid 12 year olds in this fantastic game that you NEED to learn to deal with appropriately. Do not let others get the best of you and listen to what they say and DO NOT fight back. Imagine it as a big fire and the more you fight the bigger the fire gets. Not only is it getting you and your team angry but it is making everyone on your team lose focus while the team with no team troubles could be taking an objective or ganking.
The mute button is your best friend.
Last hitting and harassing
In the lower elo's most people just try to kill the other laner while in lane. While it is always a good idea to get a kill and increase your gold, the higher elo you get up the less likely the other person will fall for your tricks. There is not much that can be said about last hitting, you MUST practice last hitting to get better at it. Learn the wind up of your champion's auto attack and know the damage your auto attacks do.
Each lane has different last hitting goals. In general the bottom lane wants to passive farm, the middle lane wants passive farm and to roam, and the top lane wants to zone the opponent while farming. Knowing this you must take advantage of your opponent and not let them meet their goals.
If you are playing an aggressive champion, you MUST ward so you do not get camped by their jungler. Also for aggressive laners or just harassing in general, the best time to harass is when they go in for a last hit, then they have to choose to either harass back or miss a last hit!
This is the end of my general guide and I will be doing more guides for each role and even some champions, stay tuned!