So Ezreal is a midgame Champ who gets his powerspike with manamune and Iceborn (or Trinity Force if you will) that's what everybody will agree on, but unlike many other midgame Champions he has a rather weak (still okayish) earlygame, but his lategame is much stronger than the one of other midgame Champsions. So a great pick against Lategame Champs, since they don't make his life too hard in the earlygame but he can snowball easier against them and doesn't fall off later.
Another good upside is his skillset, unlike mostly every other adc, he cannot really put out of the game, if you are 1-8 stay with your team, you are still usefull where a Vayne wouldn't be.

Farm, more than anybody else, you don't give a sh*t about Kills, if you get your 200 Farm @ 20 minutes, you are certainly on the winning side, even if you are 0-2-4 or something like that.
If you get camped and can see the enemy Jungler waiting to shove his Redbuff up your arse and have a Iceborn down your pockets, waste his time. Care to not get cc'd by enemy Lane and prepare to make this dude rage because he doesn't get anywhere. If they have an easy time diving you, let down your tower and swap lanes with the Toplaner except he also stays Topalane, you will get back into the game at some point.
And as usually: Farm and keep your tradegame up, you W will be your best friend, if you are under pressure, your Q an even better friend, if you aren't.

Your Q is everything you are. Don't hesitate to use your Ultimate right away, you will have a health advantage and the cast time is too high anyways if the enemy has bare sight on you.
Abuse your range, check the Q indicator to see, how ridiculous high its range is.

Melt them with your Ultimate from the backline, even if you are in enemy vision, at least 3 of 5 will not dodge it and your deathfire will already start its work from now on. Focus on your Q,but don't underestimate your w, it cannot be Bodyblocked.
If you are not in Danger to be bursted down, don't hesitate to use your E, you will have it up again in the blink of an eye with your Q passive.