Veigar's lane phase is incredibly simple. All you need to do is farm, use your Auto Attacks to create situations where your Baleful Strike can get +2 AP as opposed to +1 or look to last hit minions while tagging an enemy champion with the second hit. It's honestly frustrating to lane against a Veigar because if they're committed to farming there's not much you can do to interrupt him.

Low elo players refuse to wave manipulate which means you'll always find them pushing the wave into your tower. This is extremely beneficial to Veigar as it creates a larger threat with your Event Horizon but it almost means your farm is uncontested. It's nearly impossible to be tower dived as Veigar if you're in a decent match up so take advantage of that to safely farm until you hit level 4.

Prioritize Ability Power and last hitting so you can pick up a Lost Chapter on your first back.

This is especially important because it solves your Mana Issues while also granting a decent chunk of haste to stack easier. With the addition of Electrocute you'll be able to one shot most champions if your support is on the heavier side of damage, if you're unable to find a favorable situation it's acceptable to ignore the match up entirely until level 6.

Primordial Burst is essentially the death bell for this lane. The moment you unlock this ability, it doesn't matter how awful your support is or how bad lane is going. It just takes one combo to take a life. While using Event Horizon can be difficult, it's also a great zoning tool to close distance for your support or you can simply wait for others to land CC to chain it.

The nice thing about Veigar is that the box is the ideal set up for jungler ganks or to prevent being ganked. It's an extremely versatile skill that is the backbone of our laning, but it also represents a vulnerability. Play around the cooldown, don't be over-confident when it's down or you'll be punished. You might have one shot potential with just a simple Baleful Strike + Primordial Burst electrocute combo but only one of these skills is targeted.

Every death is equivelant to time you're not stacking, always put your life ahead of ego.

Once you've finished Luden's Tempest, there is almost nothing that can change the match up for the enemy outside of hard CC. You can continue to free farm or you can signal the end of laning phase by taking tower so that you can rotate mid lane.

You must realize that if you run Teleport it's ok to side lane as Veigar once you've taken the bot tower, but you'll want to typically go mid lane for priority on objectives like dragon or rift herald. With a large amount of Ability Power, your auto attacks will shred tower making it easier to create dead zones on the map as opposed to just spending your time bot lane. You're a scaling champion, but you're a team fight menace. It's important to be there for important objectives or you'll never get the opportunity to utilize your champion's strengths.