Early Game:
Your goal is to shove the lane as fast as possible ultimately aiming for a quick lvl 2, trading as ezreal can be quite tricky since his range is low, and skillshots can be blocked by creeps. The window of opportunity is when the lane is cleared and creeps are going in, you can position yourself and trade this way. Abuse this by reaching lvl 2 first and zoning them by going past your creeps and using mystic shot to chunk them, if they over extend you can E > AA > Q > AA. Just remember to keep poking with mystic shot and learn to push or leave the creeps untouched before recalling to not miss any exp as well as denying your enemy some exp.
Mid game
Mid game will be about grouping up for objectives, small skirmishes, and pushing. Before you group up for objectives always shove your lane (pushing it) to soak as much gold and exp as possible, because if you just carelessly group and let your lanes push, this becomes an advantage for the enemy. For skirmishes, learn who the threats are by knowing their cooldowns and their summoners, this will help you decide where you'll position yourself and who your target will be. Ezreal's teamfighting capability is one of the best because of his large AOE and his ability to reposition himself.
Late game
Late game will be about capitalizing, baron, map control, and towers. Many players I see in solo q have the tendency to not know how to capitalize on their lead which gives the enemy a chance to get back into the game. To capitalize, you will have to force fights that will go in your favor (you are an all in comp) or pushing down towers if they can't defend because they are getting chunked. Doing so will enable you more opportunities to further capitalize since they will be pressured for a baron defend or inhib defend.
Teamfighting
Ezreal's teamfighting is exceptional. His built in Flash and AOE makes him one of the best and safest AD carry, but to start playing AD, you will have to learn the basics of kiting and positioning. Most AD's will be built damage first defense last, this leaves them in a very vulnerable position. Avoiding damage while dealing the most damage is core for an AD, this is something you learn throughout your League of Legends career and it takes time to master. Positioning yourself depends if you have your E up and flash up, having those two gives you a bigger room to outplay the enemy, also your E will always be up if you land your Q's effectively.
Tips and Tricks
Use your ULT and W before teamfights to have your passive up
Use Q to check fog or brushes
E over ledges and walls
Hit Q to lower CD of abilities
Use Q after an AA to maximize damage
