Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Exhaust is used to have psuedo CC on Ez, since he has none at all, Exhaust works great. Be sure to use it effectively on champions that will shut them down, like Warwick, Yi, Xin, etc.
Ghost is used as a nice chase down skill. I used to use teleport, but I found Ghost is a lot more versatile.
Start by buying a mana crystal and two health pots. Then start building the items in order. Be sure to last hit miniCAWCAWCAWCAWCAW you know basic Ezreal stuff.
The 6th item is reserved for counter-items like Void Staff, Thornmail, Banshee's Veil. Use your own judgement to know which one.
I assume you know the basics of Ezreal so I don't need to explain his QWER abilities.