Just play Ezreal to win it's really ez.

Kite Well!
Follow the instructions in this guide, this will make your left click into attacking so that it will help kiting immensely and cancelling autos wont be a problem.

Hello! I am currently in platinum 5. Last season I only hit gold because of laziness and not wanting to play. But this season I started in silver 2 and got to plat within a month. All it takes is determination. Although I main jungle and mid, I have to learn how to play other roles too. Right now I'm learning to play ADC and Draven and Ezreal are the only two I know how to play pretty well, so I am making a guide as I learn more and more.

This is my ideal rune set up, you get a decent amount of flat ad along with some attack speed to help farming/trading etc.
An alternative may be

You may be wondering why I take oppressor instead of Bounty Hunter. It's because once you get your first core item; Iceborn Gauntlet, every one of your q's that you hit will have a slow and that procs this giving ezreal a huge early game power spike.

I take e second usually due to the fact that in bottom lane there are many things to dodge, such as morgana's q or thresh's q. It is a key ability in his skill set.

This is one of your KEY items, this item is the main reason you get oppressor in your mastery page. It gives a huge power spike right when you buy it. It increases the damage of your q immensely. Also, from this item you get nice bonuses such as the extra mana for more spammability, the armor; so your laning is easier, and cooldown reduction. The best part of this item is the slow factor, with this and your arcane shift, kiting will be a lot easier making you almost unkillable.

This is your second most key item. After your tear is done stacking you will have crazy damage from your autos/q's. stack that with your Iceborn and you will be unstoppable. Since your q procs the muramana it will help you reach your power spike along with the Gauntlet.

Ionian boots are straight forward and simple, you get more cdr; which is important for Ezreal. You may also build Berserker's Greaves, but you have your passive and the attack speed runes to compensate for the attack speed.

You may either get Dominiks or mortal depending on their team composition, but one of these are needed. The armor penetration procs with the Muramana and Sheen to do tons of damage XD. Tanks will not be hard to kill with one of these.

Bortk or Blade of the Ruined King is an important possible item for Ezreal because it gives him the needed lifesteal and does percentage of their hp. Also the active that steals hp is very good for survivability during team fights.

This item is the perfect last item for Ezreal against a team with a lot of cc. The qss or Quick Silver Sash's active will cancel any cc including Zed's ultimate. Skipping all the unimportant facts; You get damage and will not die as easily.

Flash is a must have spell for Ezreal. Although he may have his E, a double escape is always good!

Heal is an ideal second spell for Ezreal, as it may provide during sticky situations with it's heal and movement speed buff.

Take cleanse over heal when there is a lot of cc on their team. Like a lot. Enough so that QSS would not be enough to save you.

Pros

+ High Attack Speed due to passive. + Hard to Kill due to E + High Damage after Iceborn + Easy Laning Phase

- Ezreal is a champion that due to his passive can ramp up his attack speed really quickly. Due to this and the fact that his q is low mana and does a lot of damage, Laning phase can become really easy. Early on dodge the important skill shots with your arcane shift and farm and poke at the same time from afar using your q.

Cons

+ Can't catch up easily if behind + All abilities except arcane shift is a skill shot + Burns mana really quick

- If you fall behind on ezreal it will be hard to catch up. The other adc will deal a lot more damage then you since this build might take awhile to get strong with if behind. Stacking tear early and building iceborn is key for damage output. Also if you cannot land skill shots Ezreal may not be the champion for you, due to all his abilities being skill shots.

If you want to successfully use this build, it is better if you play passively in lane and just farm up to reach your power spike as early as possible. In lane use your Mystic Shot mystic shot to get the far out minions and use e to dodge the skill shots. Try to back with about 2000 gold to build tear and sheen. At level 6 you may all in if your support as any hard cc, but only on champions other than Lucian, Caitlyn, and maybe even Vayne.(As long as they are good at dodging).