Hello! I'm PeasyFlawless, I started playing this season and chose to be a Veigar OTP, I'm currently sitting in Gold 3. I feel like Veigar is an underrated champ, that I'd like to put some focus on.
On top of that, the current guides around for Veigar are either outdated, not the best or just not how he should be played.
Playing Veigar does require you to be able to play passively, have good map awareness and especially being good at csing, which is key to being strong.

His kit consists of Insane burst being Baleful Strike Dark Matter and Primordial Burst, great crowdcontrol and decent CC being Event Horizon. If you have an engager, someone to tank and distract while Veigar runs in and gets his 5 man stun, it's a free fight. Veigar's ability to delete carries with 2 clicks, or destroy minion waves in a matter of seconds makes him good, if he doesn't fall behind. Veigar is easily abused especially in higher elo.

Pros

Insane Burst

Infinte Scaling

Midrange CC

Midrange AOE

Insane Pick Potential

Veigar like any other champion has a job, Veigar needs to delete carries, CC and crowdcontrol during teamfights, and stay alive. His zoning and damage is some of the best in the game.

Cons

Bad Trading

Very Squishy

Insanely immobile

Low Range

Inconsistent damage/CC

Many bad matchups

Needs to stay ahead

Veigar is easy to abuse, his horrific early game, unreliable kit with Event Horizon being inconsistent with delayed stun, his Dark Matter is one of his only ways to deal damage, but is hard to hit. His insaely bad mobility and his only form of selfpeel being (ne of) his only escapes aswell makes his life a nightmare, your positioning in teamfights and laningphase is key to winning.

Flash is the ideal summoner spell for 95% of all champions, Flash gives Veigar some of the mobility he lacks, he can escape, dive, chase and do some sick combos. (Flash+R) (Q+Flash)


Teleport is my ideal choice as my second summoner spell, it makes your lane pressure a lot better which is something Veigar lacks early, and makes your stacks better. On top of that it makes you able to go stack toplane and being able to join the fight bot if needed.


Exhaust is one of the defensive options instead of Teleport if you're in a hard matchup against an assasin like Zed, This summoner spell will make your life a lot easier and is close to essential in some matchups.


Barrier is the logical choice if you're against longrange bursters such as Ziggs, Lux or Syndra, if you aren't in range to get your Exhaust off, and with Barrier having a lower cooldown it makes it a lot easier to survive their burst.


Cleanse is the choice against heavy CC champions like Ahri, Morgana and Lux. If you get hit by one of their stuns you're if not dead then close to.

I use close to a standard mid page.
The changes are;
Movementspeed Quintessence instead of Flat AP Quintessence. Veigar is immobile so extra movement speed is a massive help early, and 15 AP isn't much even early for Veigar so a good trade.
I personally like 2 Scaling Armor Yellows and 2 Flat Armor Yellows as they help out tremendously in the laningphase because of minion aggro. The armor will absorb the damage really well.
Flat MR Blues is great. This build, these runes and masteries are for a stronger laning phase and an insane late. After level 6 what you want to do is show lane dominance, start poking your opponent and take control, having the armor and MR really helps you out and makes your bad trading better.

The 3 main keystones on Veigar is;
TLD - DFT - SRS

Stormraider's Surge gives Veigar tremendous mobility lategame, fire a Q at a squishy enemy and it procs. Good defensive keystone, can also be used to engaged. Recommended against squishy team compositions.

Deathfire Touch gives Veigar an even better lategame burst, it's really good against tanks and is recommended against tanky team compositions.

Thunderlord's Decree is like Deathfire Touch , it gives Veigar more burst. The thing about TLD that makes it the worst keystone out of the 3 IMO, is that Veigar's short range makes it hard to proc TLD which only gives about 150 more damage around the midgame anyway. Lategame Veigar want to be in the backline, so he can't proc TLD. It's good in laning phase for poke, but the range makes you need to walk up unless they're stunned.

My reasoning behind going 18-0-12 and put points in Resolve instead of Cunning, is that Resolve gives Veigar an insanely safe laning phase, making him harder to dive. Lategame (if you use my build) it gives him around 180 Armor/MR, making him pretty tanky and making your life a lot easier.

Close choices in Masteries explained.
I prefer Feast over Fresh Blood because of the sustain
I prefer Vampirism over Natural Talent because it gives more sustain and the extra AD/AP from Natural Talent doesn't give Veigar much.
I prefer Bounty Hunter over Double Edged Sword because it gives Veigar more damage, Veigar out of all champions have the potential to kill every enemy champion, and 1,5% more damage taken isn't too great on Veigar since he's already squishy as it is.

Veigar's Passive makes him gain one stack of Phenomenal Evil Power for every champion he hits with an ability and 5 stacks for every kill/assist. Every Phenomenal Evil Power gives Veigar 1 AP.


Baleful Strike(Q) is the obvious ability to max, for lower cooldown so you can stack. Veigar gains stacks with Q by hitting champions (1 stack) and by lasthitting (killing) minions/monsters. Veigar receives 1 stack from every minion but the Cannon and Siege Minion which gives 2 stacks. Veigar gains 1 Stack for every small jungle creature (small raptors, small krugs, small wolves) and 2 stacks for every big monster (big raptor, blue, red, big krug, big wolf, gromp, drake and Baron) The scaling on this ability is 60% of your AP.


Dark Matter(W) is maxed last because though the damage is nice, it won't matter if you can't hit the W. Dark Matter has insane scaling (100%) making it one of Veigar's main ways of dealing damage, with training you'll know how and when to place it where, it's good when you're getting chased or is chasing. It's hard to hit unless they're stunned or your predictions are good.


Event Horizon(E) is maxed second, Veigar is insanely immobile, and Event Horizon is one of his only ways of escape. E is his way to set up kills it has insane crowd control, and good but unreliable CC with the delay it has.
With some training you'll know how and when to place it where, making it close to as reliable as the old E.


Primordial Burst (R) is ofc the ability to put a point in when possibly. This is the ability that makes a fed Veigar feared by everyone. The scaling on this ability is 75% against someone with full HP, for every 1% of HP missing on the target Primordial Burst does 1,5% increased damage capping out at 150% AP ratio being when the target has 33,33% or less HP.

There is 3 starting items people like to go.


This is my personal favourite because of the CDR and mana it gives it's close to a must for Veigar, the CDR is amazing early for the stacking and Lost Chapter being an amazing mana sustain item early, having the 100 AP Morellonomicon gives Veigar a great powerspike making this item perfect for Veigar.


Our second starting item is Rod of Ages, this item does give Veigar health and more mana, but it does not offer cooldown reduction. Veigar needs his 40% CDR lategame, if you do have another way to gain the 20% CDR lost it can be viable, but not recommended.


Lastly we have the powerstacker item Archangel's Staff, this item gives Veigar an insane manapool and does allow him to stack as much as he want, but come with some disadvantages. It takes a long time for Veigar to upgrade this item, it does offer more mana and ap (when upgraded) but doesn't offer the CDR. It's a decent item but I don't believe it's the best on Veigar unless you get your 20% CDR from somewhere else.

Veigar needs to have good stacks and good CS to stay relevant. If you fall behind you're setting yourself back a bit making your lategame seem further away. There is some numbers I like to follow, if you hit these numbers during the right times in the game you've stayed relevant.

60-80 stacks @ 10min
160-180 stacks @ 20min
300+ stacks @ 30min
After the 30min mark you continue to have at least 10 stacks per minute.
If you have a lower number than this you need to improve.

The ways you're going to gain stacks is by;
Getting kills/assist (5 stacks)
Hitting opponents with abilities (1 stack)
Lasthitting melee/caster minions with Baleful Strike (1 stack)
Lasthitting cannon/siegeminions with Baleful Strike (2 stacks)
Lasthitting small jungle creatures with Baleful Strike (1 stack)
Lasthitting big jungle creatures with Baleful Strike (2 stacks)
Lasthitting drake/baron with Baleful Strike (2 stacks)

On top of that csing well is important on Veigar like on any other champ. 10cs per min.
A kill is worth 14 minions, so always keep that in mind, your opponent may not be as ahead as he/she looks.
Remember you can set 2 minions up and lasthit them both with Baleful Strike getting 2 stacks, or lasthitting a minion and hitting your opponent which is even better.