Pros:
amazing burst
poke
Fuqing Iron Man...
global ult
escape-ability
self peel with gauntlet
build route makes him pretty tanky for an ADC
One of the best mid games in the game.

Cons:
Incredibly skillshot reliant, so you will need to be good at those
easy to mess up combo
Ult does like no dmg if it hits a bunch of minions
out shined by hyper carries late game
His ultimate skin ( iron man ) is severely outdated and actually makes his game play worse because it feels so clunky (trust me...) still sweet to have for those die hard ezreal fans. But now id honestly opt for arcade ezreal if i had the money to buy it.

So there are many different ways of executing combos with ezreal, which is why he will take some time to truly learn.

[*] general all in duel combo: Q. auto 2x. Q W and E into it, auto till dead or low enough to ult to finish them off.
[*] Surprise burst combo ( will require some positioning and items): hide in a bush and make sure that your ult is in line to only hit the enemy champion first, no minions. Fire your ult at them and follow up with Q W E and auto and Q's to finish them off. If done right this combo will almost always guarantee a kill or at least a flash and heal.

Ezreal is pretty good at farming if the wave is frozen and not under turret. You can last hit easily cause his auto animation is nice and clear. You can last hit 2 cs with your auto Q if both are really low.

Soo this isn't just for ezreal, it's for any adc really. I'm gonna talk about something called attack move command. Now if you know what this is ( popular names; orb step, back pedal..etc) you probably don't need this. But if you are doing this with just your cursor, constantly clicking backwards and then back on the champ trying to kite like that. Stop. There is a much more efficient and easy way of doing this. The attack move command is a hotkey bound to your keyboard ( it will be under player movement or whatever and the default is usually "A". Now by clicking A on an area that your cursor is hovered over, your character will attack the nearest enemy target in that general area at the max attack range of your champion. Sounds pretty good right? well the thing that makes this better than a normal right click auto, is that if you miss click and click A beside a minion instead of on the minion, your champ will still target that minion, instead of your champ walking towards that area (which can get you killed #missclicks). It is important to note that the command will make it so that you will attack the target nearest to your cursors area, but will not cause your champ to actually "move" freely, especially if your near a bunch of minions. SO PLEASE. DO NOT BIND THIS TO RIGHT CLICK. I BEG YOU. YOU WILL NOT BE ABLE TO MOVE INSIDE MINION WAVES. practice this in normal games and on cs before taking it to ranked. This function works best during kiting, where you can click backwards(backpedal) and then click "A" next to your feet to attack the champ that is diving you in teamfights. The better you get at this, the easier it will be to kite back backline divers while still dealing dmg. Cause the worst thing an adc can do, is run while not dealing dmg, dealing dmg is your purpose. If you have any more questions about this feel free to leave comments or search it up on youtube, i know for a fact that some youtubers have already covered this.