Xerath is a great ranged champion. He is underestimated when champions are running away. If you can master his skill shot then you can be a force to be reckoned with.

Lore:
In the ancient civilization of Shurima, the mage called Xerath practiced magic with undying passion. He believed that with enough magical power, he could gaze into the heart of Runeterra to know the secrets of history and the universe beyond. Such magic was beyond the limitations of a mortal body, but Xerath obsessively pursued a path to infinite power nonetheless. With every breakthrough he grew more and more powerful, yet not without consequence. Xerath’s increasing arcane abilities wrought havoc on his physical form. Desperate, he undertook a danger
ous ritual to transcend his dying body. The outcome would be immortality or self-destruction. Violent magic unleashed during the ritual caused devastation throughout Shurima, but when the dust settled, Xerath emerged as an ascended being of pure arcane energy.
Free of flesh and bone, Xerath held nearly infinite power at his command. However, in the wake of his chaotic ritual, the mages of Shurima feared his careless disregard for life would bring ruin to the kingdom. After a terrible struggle they subdued Xerath, but they could not destroy his ascended form. Instead they trapped him within an enchanted sarcophagus and sealed him in an underground tomb. Eons passed, civilizations rose and fell, and Xerath’s imprisonment was lost to memory. For centuries, Xerath’s vast power tore away at the sarcophagus and weakened its spell. Finally, he willed forth a burst of magic that shattered his prison, but its core remained, containing Xerath and his power within its broken pieces. Seeking to rid himself of this burd
en, he was drawn to the magic of Valoran’s nexuses and found he could absorb their power. Yet the nexuses had gatekeepers: petty mages known as summoners. Xerath knew his key to true freedom from his prison lay in gaining their trust, and he offered his power to the League of Legends.
“I have no need for vengeance. Time has brought ruin to the mages of Shuri
ma and I alone remain.” – Xerath, the Magus Ascendant

This build works great for being a nice harasser. With the cool-downs of your spells being low it allows you to just keep casting and causing pain. With is cool-downs being so low he can stun champions frequently which can help your teammates.

Pros:
Great Harasser
Great spell range
Great damage
Frequent stun
Can take a lot of damage

Cons
Mana consumption
Skill shot dependent

I choose to go with Greater Mark of Insight just to give that little extra edge in the early game. The Greater Seal of Replenishment and Greater Quintessence of Replenishment to help with the HIGH mana usage by Xerath. The Greater Glyphs of Focus help to lower your spell cool-downs to freakishly low times which help with your harassment of the lane.

Exhaust - THis spell for Xerath is great. It slows champions down for you so that you can do your E,R,Q,W,E,R,Q combo which can take hurt the champion quite a bit.

Flash - This skill can be used as an offensive spell and a defensive spell. If you need that little extra time to zap your opponents this works great. If you are in trouble it is nice to get that little breathing room between your pursuers.

0-9-21 This Mastery setup gives Xerath an overall improvement. The 9 in the middle gives xerath a nice magic resist and armor boost as well as a little heath re-gen. The 21 is a usual standard for most mage champions. Giving the champ more mana, exp boost, mana regen, and cooldown reduction.

It is vital to max out your q spell first. This allows you to harass your lanes pretty effectively by making their minions seem like Swiss cheese as well as dealing a decent amount of damage to enemy champions. Follow up by taking a point in both your w and e spells to amke your q more effective. Follow up with maxing out your e to make you stun more often and hit harder.

The items might seem like they are just the recommended items... well they are for the most part... this is the only champion whose items actually make sense on him..

Doran's Ring is essential to start your build off with. This allows you deal decent damage, have decent health, and has a vital mana regen.

Rod of ages makes Xerath a tank early game. This allows for more effective use of your W spell because he has a nice health bar as well as giving you more mana and AP.

Rylai's Crystal Scepter... slow on your E for more effective stuns as well as a nice health and AP Boost.

Rabadon's Deathcap... Super AP boost...

Then the order of the last two is based on personal preference...

Farming with Xerath is pretty simple. Q now, Q later, then Q again just to be sure. Xerath's Q is a perfect farming spell because it hits everything, not just the first thing it comes in contact with, but everything inside his skill shot.