Hey MOBAFire,
TheRealTodbrot here [thats my name on EuWest, add me if you want].
This is my first 'guide' ever, so feel free to point out mistakes or give me some tips ;)
Most important thing:

This is no 'Do this or you're a N00b'-guide, I'm trying to help you playing Xerath the way I do!

Pros:

• longranged
• 1,5sec stun on only 8secs cooldown
• low cooldowns
• great to secure or steal kills
• pretty much immune to normal dmg lategame thanks to
  Ascended Form, Mage chains and his range
• Locus of power has built-in Mpen and Ghost to melt that Galio or chase fleeing enemies!
• Great farmer once you get your Rabadon's Deathcap
• Lots of AoE
  

Cons:

• Locus of power has a long cooldown on the first few levels and you'll have to learn when to turn it on and off
• A player with high health can easily survive your burst
• You need to hit a Mage chainsed target again to apply the actual stun
• Like Ezreal you need to aim your skills

Ascended form Your passive gives you 15% of your ability power as extra armor.
Not gamechanging, but a nice bonus against that pesky little Tryndamere

is your bread'n'butter multitool thingy: harras, farm, steal their buffs, secure kills, destroy them etc. It has a pretty high range even without your Locus and can damage multiple units at the same time without loosing damage. Before casting this skillshot a visible on the ground, giving enemies the chance to dodge it. Mastering your arcanopulse is pretty much mastering Xerath.

Locus of power Locus of power anchors you for 8 seconds, increasing the range on ALL your abilities by 400 and your Mpen by 10/15/20/25/30%. You can cancel this ability by just reusing it. Nice bonus: it increases you movement speed after disabling, giving you the chance to reposition yourself. This is Xerath, nuff said.
Tip: Scare your enemy away by just activating it (its free!) without actually casting a spell

mage chains provides some nice damage, but more important: CC.
Always use this spell first, since you need to hit your target with another spell to acticate the stun. Unlike Akali's Mark of the Assassin it will only damage your foes the first time it hits, so no extra damage for you :(

Once activated, you can use your ultimate up to three times the next 12 seconds. Mostly used to kill someone quickly it can also be used to farm minions fast and safe on just a 60sec cooldown. It also provides vision over the area, so unused charges can be used to scout. If you land all three hits, you will do 825+180%AP damage!

I'll split items in 2 parts: CORE and OPTIONAL
Core items are the ones you should get pretty much every game. They will mostly increse your Damage while providing additional effects (eg. Rylai's Crystal Scepter).
Optional items will change every game, you get them to defend againts certain enemies or to increase your damage even more if you are doing well

Core:
- Sorcerer's Shoes will make you...FLY faster! The +Mpen is amazingly effective early game, so get 'em fast.
- Rabadon's Deathcap gives you a nice chunk of AP and incredible +30% to your overall AP! Must have for every caster
- Rylai's Crystal Scepter will give you some Ap, health and a 35% slow. This is the best component of the scepter, giving you more time to aim your Arcanopulse after landing your mage chains for the stun
- Archangel's Staff helps you managing your mana while increasing your damage to a considerable degree.
- Zhonya's Hourglass Ap, armor and a passive you should not forget about. Instabuy.

OPTIONAL
- Rod of Ages will give you lane sustain and will increase your survivability by a good chunk. Warmog's Armor for casters ;)
- Deathfire Grasp will help you to take down health stacking targets like Vladimir. The damage will be reduced by Mres!
- Morello's Evil Tome That Dr. Mundo activated his insane regeneration without your ignite being ready? Throw that book and lol at him
- Void Staff If they REALLY stack Mres like crazy, consider this item. Your Locus of Power should normally take down most of it
- Will of the Ancients I used to like this item alot, but spellvamp won't ehlp you if you can't survive the burst.
- Athene's Unholy Grail will make your life easier if you're missing Mr, AP, and LOTS of mana regeneration (=If you can't get blue)
- Doran's Ring is a cheap item with awesome Gold/Stats ration. Consider getting some
before finishing your shoes!
Note: If you don't need special items to survive, you should get those with high AP like Archangel's Staff (the Mana-->AP is stackable)!

Escape/Movement:

is probably the best choice for Xerath, since you are missing a gap closer/escape mechanism
is not a bad choice, but you will miss that 'flash over the wall'

2nd slot:

can often give you that last bit off damage to finish them off. Only con about this spell is its short range
is usually used to shut down Carries (both AD and AP)and to catch enemies. Usefull for meeles and Champions like Vayne, kinda bad for Xerath in my opinion
is a great pick against Karthus' Requiem and other longranged abilities, but can also safe you if you ran into a Mushroom or a Mordekaiser ult is on your head.
Ps: You can also survive ignite, but you get 50% less healing once they lit you on fire
will provide you and your Team with more mana, useful if you like spamming, are new to Xerath or lack runes

As you get more experienced with Xerath you may want to adjust your runes and masteries.
Anyways, here are my builds:As you can see, I use Greater Glyph of Scaling Ability Power and Greater Quint of potency, increasing my overall damage a bit.
Using Greater Mark of Magic Penetration is a good way to max your early game damage and melt that random Galio, since it allows you to pass most of his loved Mres.
Greater seal of replenishment will allow you to harass, farm and generally annoy your opponents without looking at your empty manabar all the time :)

30.07:
Changed Athene's Unholy Grail from CORE to OPTIONAL (thx Ryan ;)
Added Doran's Ring to OPTIONAL (you won!)
Changed Greater Glyph of Ability Power to Greater Glyph of Scaling Ability Power, like them alot better! (thx Keondre for that tip!)
Moved Archangel's Staff to CORE so poor Rabadons got a new friend!

22.09:
Just noticed my guide reached the TOP 5 for Xerath! Ty <3
I stopped playing Xerath, instalockers made me switch to support champs :S

The end!
If you really read my wall of text up there, thank you!
Feel free to rate, comment and add me ingame.
I'd love to see some feedback, be it positive or negative, as long as you tell me WHY you dislike, what to improve and stuff like that.