Xerath is a instant nuker with a lot of range. He should be use well!! with this build you should be fine by using this guide. Xerath is a champion that you can use in different ways. In this build you are using him as a nuker (like it should).

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 dangerous 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 burden, 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 Shurima and I alone remain.' – Xerath, the Magus Ascendant

For runes I take Greater Mark of Magic Penetration, Greater Seal of Ability Power, Greater Glyph of Scaling Ability Power and Greater Quintessence of Ability Power

For marks I take Greater Mark of Magic Penetration. This is one of the main runes you SHOULD use playing an ap character (especially xertah). This will give you some more early game damage.

For seals I take Greater Seal of Ability Power. You don't need to take this kind of seal, you can also take Greater Seal of Scaling Ability Power. But I prefer the Greater Seal of Ability Power for my early game damage. Its making laning and ganking a lot easier early game, which is really important for a champion like Xerath.

For glyphs I take Greater Glyph of Scaling Ability Power. This will help a lot late game. There is no need to use Greater Glyph of Ability Power because your marks and seals are quite enough damage increasing early game. If you feel like it you can also use Greater Glyph of Cooldown Reduction, this will help you to get the early stacks on your Tear of the Goddess (I highly recommend to buy your second Archangel's Staff instead of your Will of the Ancients by using this rune variation. Look into the item chapter)

For quintessences I take Greater Quintessence of Ability Power. Also this is (in my opinion) a main in my ap character rune setup.

My masteries are quite the basics of an ap character. In offense you take enough to use Archaic Knowledge . You can if you like (I don't recommend it) use Cripple instead of Deadliness . This will also mean that you use the summoner spell Exhaust instead of Teleport or Flash.
The other 21 points are going to my utility page. I use instead of some mana regen in Perseverence Good Hands . I am doing this because late game the mana regen will be like 0.5 mana p/s, and the time spent death like 30 sec! So i really recommend reading this!! The use of Expanded Mind will help with the passive of your Archangel's Staff

I start with a Doran's Ring, working on to my Boots. I really recommend buying another Doran's Ring. It will make the difference between winning and losing on your lane. If things don't go the way you want it, feel free to buy a third.

Heading up to Sorcerer's Shoes, it's really important to have your Sorcerer's Shoes by reaching lvl 6. It will increase you damage output of your ultimate.

Next is the Tear of the Goddess, it will make the durability of your laning skills easier. When possesing the item don't be to greedy, use your locus of power Arcanopulse combo twice on a minion wave for the max amount of lasthits(this combo is also very good to deal a little amount of damage on enemy champions).

With your Tear of the Goddess it will be easy laning longer. Last hit hit a lot and you will be there to buy a Rabadon's Deathcap. after this item you will be playing a lot more in the background of the game. Using your locus of power followed by mage chains and Arcanopulse will stun the target, finishing it with aracane barrage will be enough to pick up the kill without even being hurt.

Buying a Giant's Belt will help in teamfights, you will be the easiest target for your enemy team. If you are doing like i said above it will be no problem, but it's always safe to have some extra HP.

Finishing your Archangel's Staff will give you a high boost of ability power. This CAN be the moment you will sell your second Doran's Ring, just for buying your Archangel's Staff in parts. If there is no need to just keep your Doran's Ring.

Going for an Hextech Revolver ( Will of the Ancients) is for some more survive ability. If you don't feel like buying this item I will recommend another Archangel's Staff.

Finishing with Rylai's Crystal Scepter for the long range slow, and Morello's Evil Tome for the cooldown reduction.

I prefer taking Teleport (for the maximum laning time) and Flash (for killing an enemy champion or to flee from him).

You can also like I already said use Exhaust. It will be a nice spell if a trynda or xin is stalking you but you will not be in range to use it if you are in the attack position.

Another possibility is Ignite, It's deffinitely a really god spell. So if you fell like it, just pick it.

The other spells are not really necessary to use, however I am seeing a lot of Xerath's taking Clarity. THERE IS NO NEED TO. I'll defenitelly not recommend clarity!!!