Hey everyone! This is my first attempt at a character guide, so please keep the criticism as constructive as possible! My emotions are tender. I have enabled requirements to comment in order to vote simply because I would like to know what you think either way. The potential weaknesses or strengths that stand out to you, or a simple pat on the back to make me feel better. =D

This build is designed very specifically around having the ability to solo-lane, and having the ability to do it well. If you feel uncomfortable solo-laning, then you will likely want to go with a different item sequence. Something that is less expensive at the start. In that case, I recommend sticking Rabadon's Deathcap toward the end and finishing your Archangel's Staff first, though losing that ~300 ability power at level 8 can prove to be a very big game changer.

Yes, I focused Ability Cooldown runes. Reason being, over the course of the average game (about 40 minutes) the amount of times you are able to cast baleful strike with the reduced cooldown adds a MUCH greater amount of ability power than the runes ever could. On top of that, even at end game when you are level 18 and have all your items bought, the tiny amount of extra ability power missing will not be noticeable, but the percentage of cooldown remains extremely useful. Those split seconds alone have saved me in many fights.

Most of the masteries are fairly self explanatory, but let's go into why you don't want to spec into Clarity.

Every champion starts out with a bit of an issue with their mana, but if you really pay attention, there are rarely any champion's out there that have an issue with mana around level 10 or so, and that's usually around the same time you will no longer be running around by yourself. Having Clarity is mainly to make sure your early game solo-laning has no down time. The natural amount of mana restored to your nearby allies is not significant, but it is more than enough to change the outcome of team fights, and most people will blue pill after the team fight is over anyway. Even if you managed to ace the opposing team, pushing towers requires little to no mana.

So putting the point in Greed? Well, it's really just that. Be greedy! How often do you end up back at your base and find yourself in a situation where you could choose to either wait for a few seconds and get that next item, or go out on the field and get it on your next trip back? I used to find myself in that situation a lot. Depending on how the game is going, a quick way to make your way around that issue is to Teleport to the closest, largest bunch of minions, wipe them out and blue pill home and get that item, but with Greed, you'll find that the small gold increase is a GREAT boost and is a lot more noticeable than many would think.

With that said, Teleport and Clarity are a must for my play style. Being able to snag those large build-ups of minions is very important, and Clarity never stops helping.

Meki Pendant
There are a couple of ways you could go with the initial item sequence. The reason I recommend the Meki Pendant over the Sapphire Crystal is simply because with the mana potion and clarity, having more mana just feels moot. That, like everything, simply falls into personal preference, but overall either way does work well, it just feels more effective having the mana regen as opposed to the mana. It can often mean the difference between blue pilling to refill or waiting a couple of seconds and still gaining that much needed experience.

Health Potion
As is custom, the health potions can mean the difference between a blue pill and remaining in your lane.

Mana Potion
Like the health potion, this is really just bought as an excuse to stay in lane and hog experience as much as possible.

Rabadon's Deathcap
If you lane well and manage to get this item in time (around level 8 depending on the kills available to you) then you are off to an extremely great start. I prefer this path as opposed to the more common Mejai's Soulstealer because it is all static. I personally feel more relieved when I don't have a snowball item to cater to and if I do happen to die, I feel like there is no penalties to my damage output as opposed to with Mejai's when it feels like I just suffered a drastic setback in my performance. Getting this item quick will almost always force a surrender as nearly every champion you face once you get this, assuming you get it quickly enough, will die in a mere matter of seconds. This is the ultimate morale killer.

Sorcerer's Shoes
Extra damage and a bit more mobility? The logic is undeniable! But remember, don't just look at what this guide says and do it. Some games may have very specific champions you are going against and these boots may not be the best option in every scenario. I sometimes go for the Boots of Mobility. Simply because a mobile Veigar is a VERY strong asset to any team. I will touch more on that in the Team Work section.

Rod of Ages
You want to make sure to jump right into this item.

Archangel's Staff
This is what you should have been thinking about when you initially bought the Meki's Pendant or Sapphire Crystal. I feel no real explanation is needed other than the obvious boosts it gives you.

Void Staff
Ability Power is good!

Rylai's Crystal Scepter
Yet another item adding to the concept of a Veigar that can handle his own. The health bonus coupled with the added ability power simply makes you that little guy that, the moment you show up, people will know the fight was just turned against their favor.

To be very short and simple about the skill sequence you should follow. Baleful Strike MUST be maxed out as soon as absolutely possible. More damage and less cooldown means more frequent and easier to attain last hits and those are crucial to ANY Veigar build. Otherwise, your stun cools down quickly enough to stay useful without adding to that until later and you want to make Dark Matter a strong part of your rotation quickly as well.

Veigar shouldn't always be looked at as solely a nuker. He is an excellent support class as well. Remember to use your Event Horizon as a support spell as well. It is one of the best ways to save an allied champion from a certain death. Place the circle around a fleeing ally to almost guarantee their safe escape. If your Event Horizon is on cooldown, remember that your Dark Matter quickly becomes a terrifying spell, and placing one on your fleeing ally will almost always result in the champions chasing him to go out of their way to avoid running through it, allowing your ally those very important split seconds to complete a successful escape.

Otherwise, if your team is competent enough, trap as many enemies in your stun as possible, and burn them down! If you have a good make-up, you will be the hardest hitter on your team and will be vital in winning fights. If you are looking to build an extremely deadly team, keep in mind you are entering god mode if you play with a smart Fiddlesticks. With your stun and burst coupled with Fiddlesticks silence and ult, the two of you alone can destroy entire teams. As seen in this picture where me, a very skilled Fiddlesticks and a brilliant Rammus (Teemo was bad in this game) managed to take on a well played team of 5 players by staying together and utilizing our deadly anti-team measures. Also note that in this picture, my build was still in production. Imagine if I had reached full effectiveness!
http://i78.photobucket.com/albums/j97/paswerdz/4v5.jpg

That was technically a 4v5 game, but I consider it a 3.5v5 due to the lack of Teemo skills.

Be careful! I cannot stress enough how easy it is to die as Veiger if you are going against someone with a long ranged, hard hitting ability.

You want to keep your distance as much as possible, remembering to get that Baleful Strike last hit whenever it is up, but also not forgetting to take the last hits with your standard attack as well to get all the much needed gold. Try not to use your stun offensively (or at all if possible) until you get your Ult. This will keep the person laning against you feeling confident and cocky. I tend to leave the opposing laner alone until level 7-8. By that time I bring them to about 50-75% health and then surprise them with your true power when they get too close, giving you a very strong advantage as a solo laner.

Watch for those long range hits, stay passive until level 7, and push push push. Don't be afraid to take down the minions with Dark Matter. You may feel like you are losing Baleful Strike chances, but there will be PLENTY on the next wave of minions. Just make sure your Baleful Strike is, more often than not, on cooldown!

Veiger is the ultimate teammate. With his stuns to save and his nukes to destroy, the only thing lacking, his mobility, is made up for with summoner spells and items.

This build is designed to make you not that Veigar that is only useful in team fights, but the one that can face a champion one on one and still come out on top. Even vs. Xin Zhao and his charges coupled with ridiculous burst, you can be victorious. Don't be afraid to stand toe to toe with opposing champions! Make them afraid of you.

I have been able to buy out all my item slots in a few different games and every single time the results are just fantastic. Tough destruction in a little blue hat!

Again, please keep your criticism constructive, and I will be keeping this build up to date as needed.

Thanks for reading! Nuke on!