Scaling Cooldown Reduction - You need Cooldown Reduction to be able to cast your R and other abilities quicker in the late game. You would take scaling instead of regular because it lowers your cooldowns more than the regular cooldown glyph at level 9.

Scaling Health - More Health in the late game means living longer and being able to get out of more situations. The extra 215 health could be a huge difference in a teamfight. Having more health means you have more time to use your R on someone before you die.

Mana - Having more mana mainly helps for your early game. Every Veigar runs out of mana while farming with their q and this little extra mana means more stacks before you recall or having enough to stun someone ganking you when you are low mana.

Ability Power - This also helps with your early game. Extra ap means more damage you do to minions and more minions being killed earlier with your q.

As Veigar you want to max out q first to maximize your stacks from killing minions. Then you want to max e to decrease the cooldown and allow you to stun/burst more champions.

- Flash is the most important spell you want to take on any champion. It allows you to get closer to a champ to be able to stun or burst them, to run away from people chasing you, or to get over a wall quickly.

- Teleport is a very important spell on Veigar. It allows you to recall and get mana/items and then get back into lane.

As Veigar you want to finish minions off with your q to get more stacks. In mid game and late game you want to use w to wave clear the caster minions and q to finish them off or the kill the other minions.