If you don't already use smart cast, consider it for playing Veigar. Veigar's kit is a bursting kit and it is heavily reliant on landing his combo of spells in as short a space a time 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, juggle 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-attack 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 Horizonis not available, as it is one of Veigar's most important abilities, it has a long cooldown, making Veigar an easy target when it's unavailable, especially against enemies with high mobility (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 its 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.
The cooldown and active effect of Deathfire Grasp synergizes very well with Veigar's kit. Make sure it is the first to deal damage in your combo as it will increase your damage upon 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 Veigar's since Veigar's gains permanent AP from killing enemy champions anyway. if you are doing well though by all means try it.
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 Veigar's survivability against champions, especially the ones with good poking kits. 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, it can be used against Wraith camps.
Lich Bane can additionally scale very well on Veigar, one consideration has to be taken though as the Lich Bane proc can hit an enemy before Baleful Strike can land unless you prevent Veigar from auto attacking by keeping him moving around, if you keep this in mind though, it will make a fine addition to your damage output while giving you more movespeed. Works very well with Deathfire Grasp.
The Howling Abyss
The Crystal Scar
The Twisted Treeline
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.
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.
Forcing Veigar to use Event Horizon leaves him vulnerable for its long cooldown afterwards, which can be an opportunity to go on the offensive.
If you are playing a mage, avoid approaching Veigar until his Primordial Burst has been used as it can spell instant death or bring you close to it.
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, 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 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.