UPDATED TO NEW MASTERIES!!! This is my first guide. I am by no means a pro veigar player. However, i have played him enough to know his ins and outs, and feel i can contribute to people better understanding how to play Veigar.

Veigar gains 1 Ability Power for every last hit made with Baleful Strike. This is what sets him apart from other mages.

He also has an amazing burst tool through his ultimate Primordial Burst, and his utility through Event Horizon is just amazing.

They just made Veigars mana costs a load better with this patch (December 13th 2011), but he still needs to conserve mana for farm and the large amount of mana it costs to burst someone down.

I roll with Greater Mark of Magic Penetration for obvious reasons, and Greater Seal of Cooldown Reductionfor that quicker cd on his relatively long Event Horizon cd and of course for his Primordial Burst. Greater Glyph of Scaling Ability Power for dat AP, and straight Greater Quintessence of Ability Power for easy last hits to start, which is ESSENTIAL to having a good game. You could do HP/lvl seals, or mana regen, but it is up to who ever is playing really.

With the new masteries, going 21/0/9 is the best by far. the amount of AP gained from offense is too good to pass up. The damage output is amazing. Along with this, utility brings in the increased buff duration Runic Affinity and some extra mana regen Meditation for farming up Baleful Strike .

With the reduction of Veigars mana costs, I feel like rushing Tear of the Goddess is not as good as it used to be. Now there are more options for Veigar players. Rushing Deathfire Grasp can secure early game kills through Veigars burst and turn him into a true assassin. It is up to who ever is playing him, but Deathfire Grasp is definitely a top item for Veigar now.

Deathfire Grasp should be picked up early. I personally feel doing Deathfire Grasp -> Rabadon's Deathcap -> Void Staff will maximize early damage.

Grabbing a Mejai's Soulstealer if you are doing well is definitely a good idea, but never mandatory and i would NEVER buy one in ranked. The focus is on being able to stay in lane, and having a lot of burst. Rod of Ages is also viable, it all depends on the amount of harass you are getting from your opponent. If you are getting harassed hard by say Kassadin or Cassiopeia, then maybe a Rod of Ages instead of Deathfire Grasp would be preferred.

Mandatory
Flash is the most useful thing on Veigar. If you misplace an Event Horizon when escaping, or if they flash out, you are essentially useless without flash. Flash is almost always used as an escape mechanism, but has its purposes for offense as well.

Optional
Teleport for getting back to lane is a. With this in mind, you will be recalling back to buy more often than other people, because you can get right back into the action.

Ignite is also a valid choice, it depends on your play style. I like Ignite, and feel that veigars burst is just insane with it. However, if you do not want that extra dps boost then Teleport is the way to go.

With the current META game, you will be in mid lane. Start with Meki Pendant and 2 healing potion. Spam your Baleful Strike to last hit. Try to last hit with it as much as possible, and with the new patch, now you can see the amount of farm you get :) Harass with it as well, as it has a new low mana cost and can do some decent damage early on.

If you took Teleport then you can go back once you have enough for boots and more potions, maybe a Doran's Ring if you need more hp and regen. Having a few rings never hurts and is definitely benefitial in early play.

Your combo is: Event Horizon -> Dark Matter -> Baleful Strike -> Primordial Burst = dead. This is the basis to landing kills as Veigar.

If you are rushing Deathfire Grasp, then your burst will look something like Event Horizon -> Dark Matter -> Deathfire Grasp -> Baleful Strike -> Primordial Burst.

Middle lane you can net some easy kills and make this tiny master of evil pose a threat because people need to be very careful around you. The amount of burst with Veigar is quite high, especially laning against other AP carries.

ALWAYS go for last hits with your Baleful Strike. This is essential to being a good Veigar. You need the bonus ap. You also need a solo lane. Without solo you will not be fed enough to get that damage up. Don't go for kills early on unless the other team is failing at getting hits in, or they are just plain bad. Focus on creep kills, with auto attacks to harass. Conserve mana for creep kills. I only get rank 3 of Baleful Strike early game because i find it is enough with bonuses to get those last hits on minions as well as harass, whilst giving me points for Dark Matter which can 1 shot creep waves and push lanes fast and give huge farm.

One thing a lot of veigars dont do is jungle enough. Mid game you should do enough damage to one shot the wraith spawn and wolf spawn with Dark Matter. Just walk over and toss it down for easy xp and gold. Wraiths can be hit from mid lane as well, so you dont even have to leave lane! so easy. get blue as often as possible, as the cdr is awesome for Primordial Burst and Baleful Strike spam.

Let your jungler know that you NEED it though, too many times will you see a jungler just take blue buff mid game without even thinking to give it to the AP mid.

The main strategy for veigar is as follows:

Scouting:
Your Dark Matter can be used to scout bushes whenever needed. Never run into the unknown because you are super squishy as Veigar. Dark Matter has a lot of potential, remember that!

Gank:
In a gank start with a Event Horizon. Try to place the edge of the circle right beside the enemy champion, and in the direction they are moving so they get hit by the stun. Immediately drop down your Dark Matter on top of them late game, and in early game with shorter Event Horizon durations, place it in the path you think they will run to. This can be tricky, and takes a lot of practice. Predicting the enemies movement is an essential part to being a good Veigar player. After Dark Matter lands hit them with a Baleful Strike. If this doesn't kill them then pop Primordial Burst.

Primordial Burst scales very well against ap carries, so you can do quite considerable damage to them with just your ultimate end game.

Team fights:
You need to stay back. Place your Event Horizon on top of the melees running and, prevent their damage. This should also hit the carries in the back. Drop Dark Matter on top of the ranged carries, and if someone is ap blow your Primordial Burst on them and they are almost guaranteed dead. use Baleful Strike when possible. After your initial burst you become somewhat useless until cds are up.

One thing people may not be aware of is how the active on Deathfire Grasp works. It scales off of the targets current health, so you need to use it first to maximize DPS. Putting it in item slot 1 or 2 so you can hot key it easier is preferred by most players. It also scales very well into late game because it adds 3.5% more damage per 100 ability power. Late game this can crush even tanks, making it a situational active item.

Your primary focus is to blow up their AP carry or AD carry, whichever is closest and poses the highest threat. Primordial Burst will deal enough damage to effectively destroy the AP carry in almost 1 hit if you are farmed and they have a nice amount of AP. So save your ultimate for burning down the AP carry or AD.

Im still new to mobafire, and hopefully i will make a more indepth guide at some point. But this is the essentials to a good veigar. stay back, stun on top off teams to immobilize everybody, and pop your ulti on ap carries to demolish them instantly. Veigar is a great hero, with amazing burst and one of the best stuns in game. Learning how to use his Event Horizon to escape, to gank, in team fights, to save a team mate and such is what takes time to master. But once learnt it can make team fights sway in your favour quite heavily.