Veigar is one of those champions that really hate early, but also easly destroys anybody besides tanks in late. So if you have 0/3 at 20, don`t go all surrender, just stack your Q and wait for late game massacre.

I found having 40% cd reduction being very effective in late game, instead of making you one trick pony, now you just spam spells dealing 1000+ damage each on enemy heads. Obviously late game isn`t all we have to deal with, so i added some health + AP runes for easier laning phase.

Flash = Get it or die hard
Most important spell for veigar, helps you get a kill and avoid getting killed.
Ignite = Early killer
can help you finish some of those kills early, sadly, short range.
Barrier = Escape artist
Barrier is an underrated spell, helps you survive quite alot more damage. The only con is it lasts only 2 seconds, so it`s not for every enemy.
Teleport = Farmer
It isn`t the best spell, mid isn`t far enough for it to be that usefull, and late game tp isn`t that awesome as veigar.
Heal = For adc
Personaly i think it`s a worse version of barrier, yes, it can heal, and gives you slight speed boost, but it can be easly countered by ignite
Other spells = Don`t get them
Other spells aren`t worth mentioning, spells above are a better option

Oh, the Q, this the reason people play veigar. Max it out asap, use it as often as possible. For poke, for farm, for ks...
Your main damage source, but insanely hard to hit without your e, some people prefer to max their e before their w, but i prefer to have smaller chance with greater reward
This is a great counter gank spell, if used propertly, can save your life, it is also very good in teamfights.
The mighty ult, the AP carries doom, use it when you can finish someone but can`t kill him with Q or Q+W combo alone

Use Q as often as possible, try to get two minions at a time, but don`t wait for last milisecond to cast, sometimes you need gold more than a chance for reward. I almost never use W for farm, but i use E for farm, sometimes you need to stop a minion wave, you just put your stun and continue with your farm.

Well, this isn`t a guide with most details, but my main goal was to share my build with an outside world, i personaly think it`s a realy good build.