Champion strength as a mage comes from his overall high damage, the CC potential of his Event Horizon, and mage-killer Primordial Burst. This combined with his theoretical infinite AP stacking makes him a dangerous opponent as a mage. He suffers from abnormally high mana costs, low ranges, mobility, and durability, making him reliant on his allies to protect him.
If you don't already use smart cast, consider it when playing Veigar. His kit has high damage but is heavily reliant on landing his combo of spells as fast as possible; choosing smart cast will make it easier to use all spells at once, especially when using additional skills or items such as Ignite or Deathfire Grasp.
Keep track of your mana pool, especially in the early game. If you simply use Baleful Strike only to farm, the enemy will soon start to harass you; juggling between using Baleful Strike with auto attacks on enemies while still farming minions is key to dominating a lane early game.
Early ranks of Baleful Strike have a higher cooldown, so remember to also use your auto-attacks to get last hits.
An easy way to last hit with Baleful Strike is to let the tower hit melee minions twice then follow it with a Baleful Strike. Let the tower hit caster minions once along with one auto attack and a Baleful Strike.
If possible, try to finish off enemy champions with Baleful Strike. It'll give you 2 more AP, in addition to the passive AP gain after killing an enemy champion.
Event Horizon is one of the strongest stuns in the game - it stuns for 2.5 seconds at max rank and is AoE. With practice, it's easy to stun or cage at least 2 or 3 players.
While being chased through the jungle Event Horizon can be used to block off a choke point for a successful escape.
Event Horizon is effective if enemies attempt to tower dive, if you land the stun after the tower has started to target them they will suffer many hits for it often landing you kills early game.
Consider further leveling of this skill early game if the stun isn't holding enemies long enough for Dark Matter's to land. Since Dark Matter is one of the hardest hitting skills in your kit, it is another key to dominating your lane all so that you can farm using Baleful Strike with less harassment from a passive enemy.
Practice aiming Event Horizon so that enemies are on the edge and thus immediately stunned, it is vital in trapping champions with escape mechanisms such as Flash.
Always be more cautious when Event Horizon is not available, as it is one of Champion most important abilities. It has a long cooldown, making Veigar an easy target when it's unavailable, especially against enemies with high mobility and damage (like Fizz).
You can use Dark Matter's impact animation to cordon off your foes; place the spell near the champion but angled towards the direction in which he is most likely to retreat.
Starting from level 4 of Dark Matter you can use it for killing half or whole minion waves, as it instantly kills minions by then.
Placing a ward at the enemy wraith camp means you can use Dark Matter and Baleful Strike to clear it whenever it spawns for easy gold and XP that the enemy jungler is denied. Care should be taken as to missing opponents and the location of the jungler when attempting this, however.
Using your Primordial Burst against enemy champions with high ability power can have devastating effects, due to it scaling off your target's AP as well as yours. As such, prioritize mages with your ult.
An advanced tactic is to use Dark Matter before landing Event Horizon. While it is difficult to master, if you have aimed both spells correctly the enemy won’t be able to escape before the Dark Matter can land.
Another advanced tactic, you can sometimes use Event Horizon to bait an enemy with a skill / ability such as Cleanse, place the stun just near them but without actually stunning them, they may activate their Cleanse simply believing they are removing your stun and then still walk into your stun ring.
Veigar, like most mages, benefits most from building AP, cooldown reduction, and mana regeneration. However, due to his decent base damages and scalings, magic penetration in particular is an excellent stat for him.
A Void Staff is almost always a necessary item for Veigar as enemies will likely be building a lot of magic resist to survive your damage output.
Alternatively, an Abyssal Scepter can be built as a more defensive item since Veigar must come dangerously close to deal his full combo.
The cooldown and active effect of Deathfire Grasp synergize very well with Champion kit. Make sure it is the first to deal damage in your combo as it will increase your damage on the target for 4 seconds.
In addition, combined with Rabadon's Deathcap and Void Staff, it gives you the possibility to nuke even tanks or characters with about 150 magic resist from full to zero in less than 2 seconds. Building Deathfire Grasp right after completing the boots is therefore never a bad choice.
While Mejai's Soulstealer would usually benefit any AP caster, it isn't necessary on Champion since he gains permanent AP from killing enemy champions and it is a rather risky purchase considering his vulnerabilities.
Veigar can often become a target to be shut down by an enemy team, especially early game. Investing in health may sometimes become necessary to survive, whether it's surviving long enough for allied champions to peel enemies off, or to last long enough for spells to come off cooldown.
One option is buying a Catalyst the Protector, it gives health and mana for a good early game. It also opens him up to upgrading to a Rod of Ages for extra health, mana and ability power.
Spell vamp items/runes can improve Champion survivability against champions, especially the ones with good poking abilities. Though it will hinder his damage output.
If you did equip Spell Vamp, using the long range on Dark Matter is a safer option over Baleful Strike if the enemy is harassing you well, however, it has a high mana cost and 1/3 effectiveness.
Lich Bane can scale well with Veigar. In addition to the slight increase in mobility, the proc adds another nuke to his kit to be amplified by Deathfire Grasp, making him very good at instantly deleting priority targets.
Twin Shadows, while lacking the additional power, offers CDR and the same mobility and an active to catch enemies out or escape.
ZoningVeigar during the laning phase will deny him from farming ability power from last-hitting minions with his Baleful Strike as he is fairly squishy and weak at early game.
This is important because if Veigar is allowed to farm and get items and ability power, his combo will be lethal late-game, being able to instantly kill almost any champion, even AD champions if they are squishy. The only champions who can survive his combo are bruisers and tanks with a lot of health and magic resistance, and even then, it will take more than half of their health, leaving them low enough for any ally to pick them off.
Unlike other champions with stats that can increase infinitely, such as Nasus and Sion, Veigar is built with items that leave him very squishy himself. Due to this, it is imperative to avoid being stunned by Event Horizon; if you do this, burst Veigar down.
Although Dark Matter deals massive damage, it has a considerable delay before it lands. Use this to avoid the spell.
If the wall of Event Horizon misses you during placement, avoid walking into the wall as it will still stun you for the full duration.
Pay attention to Veigar's cooldowns. If Veigar uses Event Horizon or Primordial Burst (or both), this is where he is the most vulnerable. Take the opportunity to kill him as fast as possible.
If you are playing an AP champion, avoid approaching Veigar until his Primordial Burst has been used as it can spell instant death or bring you close to it.
With just a Deathfire Grasp, Veigar can use Primordial Burst to instantly kill you, not even having to use his other spells.
A common mistake amongst mages is to build Sorcerer's Shoes when laning against Veigar, when they should build Mercury's Treads instead. While the extra damage will be missed due to not having magic penetration, the extra magic resist and tenacity are helpful due to Event Horizon. The sooner you get rid of the stun, the better chances you have to survive Veigar's combo.
In fact, it is recommended to build Mercury's Treads on any champion on your team if there is a Veigar on the enemy team, as it will decrease the chances of him being able to land his mortal spell combo.
As a purely combo based mage, buying a Banshee's Veil is an excellent way to counter him as it essentially negates one of his spells, making him unable to initially unleash a full combo upon you.
If Veigar is giving you a hard time in early game if you are AP, try rushing a Negatron Cloak and build it into an Abyssal Scepter as he will no longer be able to successfully harass you until he has his Void Staff. Champions like Galio with a naturally high magic resist have the advantage over Veigar.
If you are AD, Hexdrinker is the option to build, instead.
Because Primordial Burst is dependent on the target's ability power, champions who mainly benefit from AD items such as Jayce, Talon, Kha'Zix, Zed and Yasuo are effective counters against Veigar. Be wary that unless they invest on some health and magic resist, even these champions will be instanuked by Veigar's combo, late game.
The majority of Champion damage output is magic damage, hence items such as Banshee's Veil will mitigate his damage output by a large margin. Banshee's Veil also negates one of his spells, which is vital, since Veigar is a combo-based champion.
If you are laning against Veigar as a mage, consider build alternatives that invest in relatively low ability power, such as magic penetration and cooldown reduction builds. Your own damage may be reduced, but this could well prove an acceptable trade-off to being less vulnerable to being gibbed by Primordial Burst. If compatible to your playstyle, Lich Bane would be a good pick up as while it does not give the highest raw AP it adds substantially to your burst.
InterventionKayle can leave allied champions completely immune to Veigar's combo, making Kayle somewhat of an indirect counter to him. But if Veigar decides to focuse Kayle herself, if she is stunned by Event Horizon, she can't cast Intervention on herself, and will fall to his spells just like any other AP champion.
Champions like Sivir and Nocturne can use their spell shields to avoid being stunned by Event Horizon, and better duel Veigar. Especially Nocturne since he can dash to Veigar and kill him easily, and his Paranoia make difficult to Veigar to chain his spells on a teammate, making him one of the best champions to get rid of an enemy Veigar.