I've recently started to play solo queued ranked games and decided to play most of my ranked games with Veigar, as I can play him the best out of any other champions.

This is only meant to be a simple guide - it caters to those who already know how to play Veigar. There are other excellent guides already on this site, and they do a better job of explaining how to play Veigar.

Veigar is often overlooked as an AP carry. Most people would go for Anivia, Annie, Kennen, or Kassadin, and they are all excellent choices. However, Veigar can carry team really well as well.

I hope you guys will know the true potential of this tiny mage!

Above is the rune setup that I use.
Pretty much runes dedicated to AP carries can work well with Veigar (Magic Penetration, AP/LvL, MP5)

I've found out that Veigar is really effective when you go for cooldown reductions, hence the cooldown boots and the kindlegem for added HP and more cooldown.

Maxing up your Tear first is important, as without it, Veigar has a really low mana pool.

After my Tear and cooldown boots, I tend to save up money to buy the Needlessly Large Rod first. After that, your Veigar will start nuking hard and people would start noticing you and will focus you. Hence, the kindlegem for added HP.

The rest of the build is pretty much self-explanatory. Archangel's staff for more AP, and Banshee's veil for survivability.

Usually, when I get my Rabadon's death cap, my AP would stand around 350. After I finish Archangel it will be around 500-600, which is plenty.

I pretty much max Q and E (stun) first, while getting a W during level 4.
Maxing your stun is very important, as it increases the duration (2.5 second at lvl 5, which is a very long time during a team fight), and it helps you land your W.

Your W scales directly with your AP, and even though you are lvl 13-14 with a lvl 1 W, it is still a really strong nuke.

Regarding using your E to stun, make sure you place the EDGE of your E on them, or a little bit behind them so that when they retreat they'll hit the stun. This is what differentiates the good Veigar players against the bad ones. Usually, I follow up the stun with a W and a Q just to harass. When my stun is max, I'll do Stun -> Q -> Call W -> R-> due to cooldown reduction, your Q should be back again.

During team fights, I usually focus on their Carry / Caster and unload the combo above. Make sure you stay behind your group at all times as you are really squishy.

I choose Teleport and Flash.
I use teleport mainly to save people from ganks, or to gank someone when they are having a one on one fight.
Do not use teleport to quickly go back to the tower during the laning phase. Use it only when the enemy is on top of the tower with their creeps and your creeps are nowhere near your tower.

Teleporting to a minion during a one on one can quickly turn the table around in a fight, and your teammate will appreciate you as you kill the other champion and proceed to get their tower.

Flash and stun is your main escape tool. Stun should be plenty to escape, but when it doesn't, you'll have flash as well.

You can use flash aggressively as well. You can use it to get closer to a running enemy to stun them, or to flash in and do a quick Q -> R combo when the enemy doesn't suspect it.

I hope you guys will try out this build and realize the true potential of Veigar as an AP carry and as a support as well with his long AoE stun.