Ezreal is by far one of the most interesting, and enjoyable champions to play. Here, I will state MY way of playing AD Ezreal, and giving some tips on playing him.

Early game with Ezreal will make or break him.

Ezreal needs to be pretty farmed in order to get the damage output that he truly needs, and as you can see, this build is quite expensive.

Go to the Bottom lane with a support (preferably a healer.)

It is okay to harass with your q, but do not play overly aggressive, as you will be quite squishy early game. If you can, get most, if not all of your last hits and you can start the steamrolling during your mid-game.

Mid-game is where you should start trying harder to rack up kills. Get your jungler to gank if possible, and look for opportunities to snipe with your Trueshot Barrage.

This is your baby!

Late game Ezreal is very powerful!
Team fights - single out a squishy champion and unload your cooldowns on him. Use your W ability to buff your teammates.

Always stay behind the tank - Ezreal is very squishy, and until his Frozen Mallet, he should be played very carefully.

Wards are what make Ezreal's ultimate matter. Place wards at Baron, Dragon, and down the river to maximize vision.

Ezreal's ultimate is an amazing stealer for neutral camps. Dragon, Baron, and neutral buffs are what you want to steal. Remember, stealing is all about timing.

Keep the neutral buffs on you as much as possible. Red and Blue make a huge difference in Ezreal's functionality.