Pros:

High damage burst
Difficult to chase
Fantastic zone control
Infinitely scaling
Makes enemies salty

Cons

Garbage laning phase
Relies on farming a lot
Unreliable cc against certain champions
Qss makes life difficult

Your entire laning phase consists of trying to either kill 2 minions with 1 Q or hit the enemy with your Q, using other abilities to stack your passive is basically a waste of mana, the end goal is by the time you reach level 6 they should be low enough to kill with 1 combo if you have been poking and farming efficiently, killing 2 minions with 1 Q should always be the priority and its easier than you would expect after some practice, without any items your combo will probably do roughly 400-500 damage, when playing veigar you should always have a rough idea of how much damage your combo does so you know when you have lethal

What I love to do here is start to roam bot lane and burst the enemy adc/support then go for dragon with your team, being with your team makes veigar a lot more effective because it makes him a lot harder to engage on allowing you to safely get picks on enemies who try to get in your teams way.

You have long range so you just stand at the back of teamfights, by this point in the game you don't need your ult to kill most squishy champions in the game as usally a W Q does enough damage so you save that for someone who reaches the backline to kill you as landing your ult is a lot easier than your W, if an assassin comes to the backline usually a Q + R is enough to just kill him.

Just a penta I made with this build and runes: https://plays.tv/video/5a2b23fc2b7aa2292d/phenomenal-power-?from=user