WARNING THIS GUIDE IS LONG,like me hehe :D.

To most, yordles do not conjure images to be feared. The easygoing half-pint race, though fierce, is often regarded with some degree of joviality. Every now and again, however, a yordle turns so bad that, even at its small stature, it strikes terror into the hearts of others. Veigar is such a twisted yordle - a master of the magical black arts and a corruptor of cosmic energy, making him one of the most feared sorcerers on Valoran. Veigar was once one of those unusual yordles who chose to trade with the outside world. Imprisoned in the city-state of Noxus for years, Veigar slowly went mad in isolation from his people. He eventually escaped, but instead of returning to Bandle City, he sought tutelage from dark wizards across the land. Now he seeks to end all conflict on Valoran, by bringing all of the city-states to their knees, regardless of affiliation.
"Who says evil needs to come in a fearsome-looking package?"

Veigar the Tiny Master of Evil as his name states is evil now we continue

LoL=League of legends
MP=Magic Pen
AP=Ability Power
OoM=Out of Mana
Back=going back to base or backing up
utli= ultimate move lvl 6,11,16 move strong
regn= regeneration
AD=Attack Damage
MS=Movement Speed
LvL=Level
MR=Magic Resistance
OP=Over Powered

Pros

Amazing nuker
Great in all fases after lvl 3
Stun if placed correctly can trap there entire team, hard very very hard.
Fun

Cons

Squishy untill late game with Rylai's Crystal Sceptereven then still squishy
Hard the first few games
Targeted first if teams smart(this is why i play solo que more i can carry whole team)

Runes

For runes I decided to choose the best early game runes since thats when Veigar is at his "worse"( even though he is strong)

Greater Mark of Magic Penetration: help Veigar out the entire game with its MP

Greater Seal of Replenishment: i choose this over the mana per lvl because 1 Archangels Staff fixes mana forever, so you only need mana early game

Greater Seal of Replenishment: same with the Seals

Quintessence of Health: 90 health never hurt anyone help with early game survivability

Masteries

Standard mage Masteries nothing new here. I am looking into 9-21-0 since you can get some extra Ap% with some life I'll edit if i find it better.

Skill Sequence

Basicly u want to Max out your ulti when ever you can(no shock there) then you want to max out your Baleful Strike so last hitting becomes easyer, Veigar gets 1 AP for lasting hitting a minion with it and 1-5 for killing a champ(depends on lvl).

Summoner Spells

Best

- I would recommended this for any AP carry/nuke this helps you run and get in for that last spell u need to get in its just a great spell

- Also a great spell for mainly anyone this can piss Dr.Mundos and Tryndameres off as they ulti. And it is great for finishing a runner off.

- This spell is great for anyone it lets you run around like a ghost(hence the name) letting you escape or chase, only change for Ignite Flash is a must.

= This is bye far one of the best summoner spells out there, but often tiem i forgot i have it and dont use it.

Good

- I can see this working if you have no mana regn

Clarivoyance - only get if you premade and you have no support champ, since Veigar can spare the summoner spell, to get it or if you pro with it.

- If you have trouble with AD carries

- Veigar is slow,310 MS, this helps with getting around the map

Worse

the rest are at best mediocre for veigar

1.First start with a Doran's Ring and a health pot with dorans and runes you should have an extra 200 health :D

2.You want to go back only when you have around 1300 so you can get boots and Tear of the Goddess with this you should have enough mana for your combo when ever you want it

Then you pretty set for early game you should have at least 50 AP without any major AP items

3.You want to build your Archangel's Staff next not that surprising
many Veigar players like to go Meja's Soul Stealer, i have to disagree the second you get it people will notice and target/gank you more, unless you are pub stomping there graves like you 15-0 then get it but its too risky for Veigar in my opinion.

4.Your next option depends on the game and que you did
Solo que: i would suggest getting another Archangel's Staff unless your doing **** tehn get Rylai's Crystal Scepter

Premade que: i always get Rylai's Crystal Scepter since most likly the team you're facing is premade and they target you

5.Then get Rabadon's Deathcap pretty self-explanatory huge AP boost

6.Now just do the reverse of what you did in step 4

7.Now depends on enemy team most of the time i dont get to this stage since either i am domination or my team fed so dont expect to get this far unless premade

Defensive Vrs heavy AP

- the only good full defensive item for Veigar

Defensive Vrs Heavy AD

Thronmail- can rly hurt those Master yi that target you

Offensive MP

Void- gives great MP which can really help those smart tanks

Offensive AP

- only get if their team isn't stacking MR

Early game lvl 1-6

With Veigar you can take any lane but I prefer side lanes since your early game you cannot 1 combo an enemy to death yet...

Your early game is quite simple last hit with Baleful Strike and try to get the enemy champ(s) to 1/2 health so at lvl 4-5 you can kill or make then go back. Some Champs i would approve of laning with is anyone with alot of burst damage(like your self), Ryze, Annie, AP Master Yi, Pantheon, Sion, or any burst damage champs your double burst will kill them fast

Mid Game lvls 6-13

This is your stage. You have your full combo ready and can destroy any squishy in the game

Veigar Combo

1. Event Horizon hit them with the edge so they become stunned
2. Dark Matter you have to predict where you will get the stun before hand9only for early lvls)
3. Baleful Strike A nuke
4. if there low enough use Primordial Burst to finish
5. if they run before you can Ulti don't case your stun has to long of a CD but they will come back without blue pilling since they forgot your burst you kill them then

Mid Game Continued...

So around this time you should have at least a Archangel's Staff if you don't, say u got meja's then dont worry. Mostly you job in mid game is to farm Champs thats your job its ok if you ks, fed veigar is better than a fed Karthus since he can 1 shot a fed Karthus most of the time people can't really catch them but call its ks

Late Game 13-18

You lose a bit of your power late game since people now are stacking MR to counter you. But for there AD and AP carries there just dead meat i 1 shotted a Fiddlesticks with my Baleful Strike and he rage the rest of the game on how Veigar is OP, i was fed 15-3.

I am going to improve this guide if it does well and i am no matter what going to add a section for all champs vrs and with Veigar

ALSO
thanks for reading this is a long guide I think...
and a few of the icons dont show properly im fix that soon
plz tell me any improvements you think i should have