Hey guys! I am BlackStarShoot3r, I am a simple player here in League of Legends, and I am going to show you how to play Xerath AP mid.
Xerath is my Main hero and my most favorite one in the game, he has a nuking potential, long range artillery and burst damage.
Xerath's key weaknesses are high mobility, silences and those with a gap closer or dash to dodge his skills.
He is a fun champion and if played right, can single hadendly burst the entire enemy team without knowing what hit em in the face.

For Xerath you should run a 21/0/9 masteries.
You need to be Offensive on your customization build and item build. If you are not offensive, you don't deal damage.
Your runes serve a similar goal: Magic penetration,Ability power are your key elements to max out on Xerath. Which is why you need Magic penetration marks, Ability power(+per level) marks & glyphs and Abillity power(Flat) Quints for your offensive punch.
Your secondary elements to max out are: Durability, mana regeneration and cooldown reduction.
You can always get Health per level seals & magic reist per level glyphs instead for defensive purposes, but keep everything else the same, else you wont deal damage, so let your item build handle that.

For summoners spell your choices vary:
You can get Flash & Ignite, which are your most primary.
Flash will help you escape enemies or chase em down.
Ignite will help you finish off enemy champions.
Other spells can also help you in that regard:

Ghost will give you more movement speed
Teleport can help you move across the map and gank faster
Exhaust will disable your enemy for more damage, or to let you escape.

For every engage you start out with your E to mark an enemy for your stun, then a Q or R(If you're level 6+) to trigger it.
An awesome trick is to activate W, throw a quick E & Q and then deactivating it. It will help you poke your enemy and deal severe damage to them.
Finish them off with an E & R combo when you have the chance.

For Xerath, farming is easy as pie. Use your W to increase your range on an upcoming minion wave then Q the hell out of em, head a bit back and Q them again if you dont finish them off in the first attempt.

Xerath brings a huge teamfight pressence in a teamfight, especially from long range.
His AOE ult can bring him up to par with many other AOE nukers like fiddlesticks, but is best to pair him up with Galio who can AOE taunt them in the center for Xerath's ultimate, or Orianna for her Vacuum ultimate.
Also, those with AOE stun or knockups on their ultimates like Malphite or Lulu's ultimate will also allow Xerath to net an easy ultimate.
So if you have the propper team comp, Xerath can easily Pentakill/Ace your enemies, especially when he is fed.

For Xerath, he is really good at Long range Sniping(If you have the skill) and bursting down enemies from afar, but he is not doing so well at chasing oppoments due to his mobility, although his W makes up for that by giving him long range and some movement speed when toggled off.
He is also weak vs Players who can dodge his abilities with either a dash or gap closer, so someone like Ahri or Leblanc can easily counter Xerath.

To Sum everything up: Knowing When and Where to land your ultimate is a must! Positioning is what you mostly need, so that you can be safe against enemy assasins who will definetely try to kill you.
That's all there is to it. I hope you enjoyed this guide for it was a pleasure and an honor for me to make it.
See you on the Fields of Justice!
BlackstarShoot3r, out!