Champion strength as a marksman comes from his versatile kit, high mixed damage, and attack speed steroid from Rising Spell Force. His Mystic Shot, Essence Flux, and Arcane Shift have decent range and good utility, encouraging a caster playstyle, and his Trueshot Barrage can deal high burst damage to multiple targets. However, he is very reliant on landing his skillshots for most of his damage output.
Ezreal has one of the lowest base healths at Level 1. Utilize the range from your skills to keep yourself safe.
By aiming Mystic Shot in brushes and watching your cooldowns while listening for Mystic Shot's hit sound, you can see if enemies are hiding in a brush.
Keep an eye on your Rising Spell Force stacks and whether they increase/refresh. This aspect allows you to check brush with Champion other abilities as well.
Ezreal can utilize the Spell Weaving and Blade Weaving masteries to stack up a fair amount of extra damage with successive spells and auto attacks against enemy champions. However, players must be more aggressive and ensure that they land their skills.
If attacking a tower with an ally, you can use Essence Flux on them to boost their attack speed. Hitting the friendly champion will proc Rising Spell Force, granting you attack speed as well.
In the lane, Champion early burst damage and poke is very high. Combine this with a support or jungler's crowd control to get some kills.
Trueshot Barrage can be saved for teamfights or 1v1 situations to finish off enemies as they run away. Since the range is global and does a massive amount of damage you can kill low health enemies with a well-aimed ultimate.
Never forget that Trueshot Barrage is global and you may be able to snipe an enemy champion from all the way across the map if you have good aim. You can also use it to soften up an enemy that you are aiming to fight.
Having teammates with good CC like Leona or Amumu can make it much easier to land your skills and make the enemy take the full brunt of your Trueshot Barrage.
If you decide to snipe a fleeing enemy, make sure they don't have any sort of heal, shield, or invulnerability.
While Trueshot Barrage has high base damage, the falloff could be the deciding factor in getting a kill; to get the most out of it, try to hit your target without it hitting minions.
Use Trueshot Barrage when the enemy has no vision of Ezreal so that they will be unable to warn their teammates.
Note that Trueshot Barrage can be seen through the fog of war, so a wary opponent can watch for it and avoid it from a distance.
Trueshot Barrage has a channel time upfront and is easily dodged by skilled players. For this reason, it is often a good idea to use it to hit an entire team immediately after the battle starts, dealing significant total damage and granting multiple stacks of Rising Spell Force.
Trueshot Barrage is especially powerful in Dominion, delaying enemies' attempts to capture your towers and buying crucial time. Due to its relatively low cooldown in conjunction with Mystic Shot, use it wisely and use it often.
Smart casting will give you a faster response time, allowing you to hit more abilities.
Smart casting Arcane Shift can help you dodge a lot of otherwise deadly situations.
Last Whisper complements Ezreal for Mystic Shot and attack damage. While less-useful for regular auto-attack than The Black Cleaver, the armor penetration is the strongest against mid-high armor stacking champions, it is an amazing item against tougher enemies. Its low cost makes it an affordable purchase in the early-phase. However, it's not exactly suitable for ability power and/or hybrid builds as Youmuu's Ghostblade is.
You can play Ezreal either as a ranged physical or caster damage per second depending on how you build him. Additionally, a burst caster build could potentially be viable on him, using a Deathfire Grasp and a Lich Bane to burst down squishies easily.
Physical damage per second plays like a ranged damage per second, utilizing autoattacks, Mystic Shot and Trueshot Barrage for burst damage, and other abilities for utility and supplementary damage.
The casting of Mystic Shot procs Sheen's damage buff, which is then applied when the shot hits the target, thus increasing its damage.
If you miss Mystic Shot, auto attack the enemy once before casting Mystic Shot again. The same applies for using other abilities before casting Mystic Shot, as not using the Sheen can decrease your DPS considerably.
Within the preparation phase of Dominion in the early 1:20 minutes, Ezreal can start collecting Mana with Tear of the Goddess by keeping every ability on Cooldown. This can serve as a minor improvement for the early phases.
While the bonus Mana pool of Archangel's Staff and Manamune are the same, they complement each other very well. Getting both requires a high level of farm though. Nevertheless, each item is very useful if quickly farmed and can be a fundamental part of most builds.
Ezreal cannot trade fairly during close combat and relies heavily on poking. Having a champ that can dash or blink towards him (i.e. Xin Zhao, Diana, Irelia) would cost Ezreal his blink to run away from the team fight and be isolated from the defending allies causing his death.
Pure AP Ezreal suffers from a weak early game; his burst is very mana-intensive, he loses his only non-flash escape-skill when using Arcane Shift offensively, he cannot reliably push a lane and he lacks any kind of crowd control effects. In exchange, he becomes a very high damage dealer in the mid and late game due to his high AP-scaling and massive AoE-damage. In this case, it is even more effective to dodge his skillshots by moving erratically.