Farming:
As Ezreal your Q is your main focus, throughout the entire game and every aspect of it, even farming. Whenever you see minions that you don't think your auto attacks will be able to kill, or be fast enough to get, your Q is a great utility for it. I especially prefer to always use my Q on the cannon minions to ensure that I don't miss them.

Poking:
Throughout the entire laning phase, you wan't to make sure you poke the enemy laner as much as possible using your Q. How much an Ezreal pokes early will determine a bad Ezreal from a good Ezreal. As much as I've played Ezreal, I've also had to Vs a great amount of them, and their is a huge correlation to how much they poke down early, and how they do throughout the rest of the game. You wan't to try to always position yourself early where you're behind your minions to try to avoid their poke, and then be able to step out, hit a Q, and then step back behind your minions as much as possible.

The Q:
The number one part to winning any trade is to use your Q as much as possible. In a trade you wan't to use your Q everytime it comes off of cooldown since it is most of your damage.

The W:
The W is an interesting ability as this one isn't the worst if you don't hit the enemy with it. In most trades depending on your support, or if your jungler is there, it may even be best to completely avoid the enemy with your W and hit your teammates with the W to give them the attack speed buff instead, as the W doesn't do much damage, and you'd gain more by giving your teammates attack speed instead.

The E:
This one is where I know a lot of people may disagree with me. Depending on the situation of the trade, your E can be used to hard engage, or to disengage. This one is where you need fast thinking, and know what point you're at in the game and know how much damage you do. If you think that you have enough damage to be able to full on engage and then kill them and be fine, then going aggressive is the best way to do that, however if it seems like the enemy is stronger than you are, its good to just get some poke off with your Q and back off with the E if needed and wait for an opportunity to engage and finish them off.

The Ultimate:
Now I know a lot of people always want to try for those cross map ultimates to try to snag a kill if they're able to, but this isn't a good idea. Your best bet is to only use your ultimate in a teamfight or just a normal trade bot lane. During a trade a good combo to do is to hit them with the Q, then E away from them to a safe distance, (And also preferably in a bush if possible to ensure safety and give them less time to dodge) and then use your ultimate on them to lower them down a great deal and finish the trade with your Qs.