AD Ezreal: A lot of Ezreals try to only use Q for damage and pretty much forget they have auto attacks, you should be using primarily auto attacks if you can and using Q to keep your passive up, max E second for the kiting, avoid building tear if you can or if you do just realize it is not a power spike and you are now committed to farming up for a while before you can fight, use W on your allies to give them the extra attack speed and stack your passive quickly in team fights and when taking objectives, hit things with Q on the way back to lane to reduce your ult CD if it isn't up, use ult on other lanes if you see a kill/assist opportunity.
AP Ezreal: You aren't super strong early and don't have reliable wave clear, farm up as much as you can in the laning phase since late game you do incredible damage to entire teams, you can burst squishy targets and then turn around and pump out sustained damage for the rest of the fight, get Lichbane after you have some base AP, not as a first item. You are extremely safe in lane since you can farm up with Q so you should be able to get farm pretty easily.
Also never use E to start a fight.