Hello, I am WhiteSheepz a silver Xerath main. I have played Xerath for over a year and wish to share what I know about the champion. At his core Xerath is basically a walking mortar- he hits you at range and pokes you down. My guide should hopefully give you some insight in how to play Xerath effectively and learn the champion.

Pros:
Long-Ranged
Good Poke
Good Late Game Scaling
Decent at Stealing Baron/Dragon
Good Sustain

Cons:
Has to charge up Q leaving him open to attack
Immobile
Sometimes hard to position well
Relies on team giving vision
Very Little Escape

Arcane comet is a solid rune to go on Xerath as it is a small AOE global damage to wherever your ability hits, this allows for you to cast abilities and deal a slight bit more damage to enemies while poking them, this also has good synergy with Xerath's ultimate.
Manaflow band is used for the simple reason or giving Xerath move mana throughout the early game meaning that he can uphold his sustain and poke down his enemies in lane without risk of having to back early and recover mana.
Absolute focus is fairly important to Xerath as it allows for him to poke at his enemies and deal extra damage while he is above 70% of health, this means that as long as you stay out of the enemies range you can make full use of your extra damage and control the game from your side of the map.
Gathering storm is a rune you go to ensure that your late game is strong, as you gain ap throughout the game as Xerath it means that continually a longer game will be better for you as this ties in extremely well with Xerath's mid to late game scaling.
Cosmic insight it what you take just for the raw stats, they all help Xerath in almost every way- in particular the CDR as it means that Xerath is able to be a constant threat to his enemies and they always have to engage with the risk of his abilities being up.
Magical footwear is taken to grant Xerath the extra movement speed, as you will be going Luden's first this means that you can get some movement speed without having to cash in on boots and slow down how long it takes for you to get Xerath's power spike. The movement speed is greater than regular boots so this also helps deal with Xerath's lack of mobility.

For your abilities you go for your Q first for the poke throughout the entire game, it is the bread and butter ability of Xerath's kit as it has a fairly long range and is fairly easy to cast. When using the Q you must remember that it slows your movement speed and by charging you only increase the range. The Q is classified as a beam so abilities such as Yasuo's wind wall cannot block it- similarly this ability has no difficulties going over terrain. Typically you use this to poke enemy champions or forcing them to move in a certain direction to avoid it allowing for a setup by your teammates to go in for the kill. The Q is also fairly good for wave clear as it passes through minions and champions allowing you to deal damage to the entire wave and potentially the enemy champion as well. The range of the Q exceeds that of the turrets so you can finish off an enemy that may be recalling underneath one.
The W is the second ability that you upgrade, it is fairly easy to hit as it is in a circle shape, the enemies closer to the centre of the W take more damage however an adequate amount of damage is still dealt as long as it hits. This ability also grants some vision where it is cast and slows enemies that are hit by it, usually you would use this ability to slow an enemy allowing you to hit them with your Q as it would potentially negate the slow on yourself allowing you to catch up, this also helps with hitting your E. The W ability can see good use when you think that the enemies are taking dragon or baron and you have no vision as you can cast this, see what its health is then charge up a Q for a potential steal. The W in combo with the Q at around level 10 can usually clear an entire wave in one go.
The E ability is the last one you upgrade however it is also vital for Xerath, this ability is a stun that fires in a straight line, typically this ability is used for escaping enemies or preventing enemies from escaping you. The low cool-down on this ability also makes it fairly handy to use for clearing waves when used along side auto attacks. A good use of the E would be to stun an enemy then quickly go to your ultimate, by the time the E stun is up you can hit around 3 of your ultimate's shots. After this it would be best to cancel your ult and fire a Q and a W or simply back off if they are not already dead.
The R ability is a long range artillery shot, this ability is amongst the longest range abilities in the game only being bested by single line shot abilities such as Ashe and Ezreal ultimates. This can be used to pick up kills on fleeing enemies or to barrage a lane that is in trouble or aid a teammate in getting a kill. The first upgrade of this ability fires 3 shots and for each level up it fires one more. There is a brief moment where a shadow from where your ability is landing is shown- the enemies will use this to try and dodge so it usually helps to fire one slightly behind them to force them to dodge towards a teammate. The shots grant vision when you fire them so after the first shot you are able to land the following ones better, the shadow from arcane comet looks fairly similar to Xerath's ultimate so you can make enemies dodge the arcane comet into another one of your ults. The ultimate is great at stealing baron or dragon as you don't need to be anywhere near either of them to cast it and as it shows vision when you do fire it you get a good idea of what the target's health will be allowing you to time your shot and get the steal.
The passive ability of Xerath allows for you to restore mana around every 12 seconds with an auto attack, this allows for great sustain as you can constantly get your mana back after a combo. The mana regained is doubled against champions so poking with Q then auto attacking basically refreshed your mana used meaning you can stay in lane and the only real loss is the enemies health.

This is what I would typically use in a game, Luden's is really important for the early game advantage and I build this almost every time first item, this item allows for you to get extra damage on each minion for clearing the wave with it's unique passive, the ap damage, mana and cool-down reduction are also vital in allowing you to stay in lane and keep the pressure on the enemy team. Sorcerers shoes are good for the early magic penetration as well as movement speed, Xerath is fairly immobile so these allow you to get into position and deal extra damage early on. Morellonomicon has grievous wounds meaning that enemies have 40% reduced healing for 3 seconds after being hit by one of your abilities- this is really good for Xerath as you can poke them down with them not being able to recover fully by the time you launch another barrage of spells. Usually I go Rabadon's in this particular place as it means that Xerath gets a huge boost in his ap damage output, at this time in the game this damage is vital as it means that you should be able to do around half of a squishy champions health with a single q meaning that your tanks wont be shredded as easily by the enemies adc as well as helping you to get kills and considerably assist you team in finishing off many enemies. Void staff can go in the order I have put it or swap it around with Rabadon's either way it gives you a huge amount of damage due to the magic penetration meaning that your enemies health gets shredded away far faster than it usually would. In the position for the last item I have put Liandry's as it has a burn effect and also boosts your damage the longer you are in combat, the burn means that after you ult an escaping enemy the extra damage over time can finish them off just when they think they are safe whereas the extra damage per second in combat means that as you stick around to help your team longer you do more and more damage, this is usually a deciding factor in games as once you have Liandry's your team's damage will be significantly higher than the enemies and unless you are considerably out of position you should win most team fights. In some cases however Liandry's is not a good item to go, for example if the enemies have a heavy AD comp you should go for Zhonya's as it means that you get extra armour and cool-down reduction so you can throw out spells faster and take more damage, it is usually wise to get an item like this early on if you are against a champion such as Zed as withstanding the AD damage is core to your survival and not throwing the game, the unique active of this item would also let you ignore pieces of damage that would be thrown at you making it great for dodging high damage skill shots. If against heavy AP I would build Banshees veil instead of Liandry's or Zhonya's however as it allows you to ignore the damage of 1 ability every 30 seconds and gives you extra cool-down reduction and magic resistance meaning much the same as Zhonya's in the fact that you can stay in lane and dish out more damage. If you are confident that you can win lane consider going for the Dark Seal and upgrading it at some point in the game as that is a great item for pressing your win and snowballing the game. If you are going Xerath support I would consider going Twin Shadows for the vision and slow so you can hit abilities easier as well as going spell-thief's for the gold, other than that I would stick to the normal build as support Xerath is mainly there for poking and zoning rather than for his stuns and cc.

-When banning ban one of who is set as a large threat, typically Katarina while still learning how to play the champion, when you are a bit more used to Xerath then ban a champ who is of more of an annoyance. Sometimes it is a good thing to play against immense threats as it means that you can learn to control your temper and also know how to react in better situations.
I would suggest that at level 9 get farsight alteration as it will allow you to know where the enemies are ahead of time ready for a baron or dragon steal, placing it from a distance in a bush behind the enemies lets you cut them off if they retreat while also providing safe vision which is really important for Xerath.

-Some of the notes are just the descriptions in the chapters section, they are simply there so you can see the images while reading.
-I am by no means perfect at Xerath so if you believe parts of this guide could be improved or if I have missed any particular things that you can do with Xerath please let me know in the comments so that I can add them.