As ezreal, Just keep poking the opposition with your Q and auto-attacks. Save your E for situations where you need to avoid getting CC'd.

Use the lane brushes as much as you can to make sure that you can land your poke on the enemy team. This will allow you to accumulate a lead and shove the enemy out of the lane.

During neutral objective fights, your main goal is to make sure that you can poke the enemy team out before the major Smite fight. This way they won't be able to do anything and will die if they try to all-in.         As ezreal, Keep your E for situations where you need to avoid getting CC'd. Use the track brushes as much as you can to make sure you can put your poke on the enemy team. This will allow you to accumulate an advance and push the enemy out of the way. During neutral objective fighting, your main goal is to make sure that you can pull the enemy team out before major Smite combat. In this way, they will not be able to do anything and will die if they try to do everything.