Hey man! Veigar was also my favourite character when i begun, let me help you!
I don' t want to dwell too much in texty stuff, just know that Veigar is a burst mage: high damage, target selection, quickness and mostly be wary to never get caught!
He has a weak early power, but escalates terribly well in lategame; the first thing to do is farm your lane while being safe, using the Q to last-hit minions and obtain AP. AP is the most useful stat for Veigar, but since he gains some by his own and at the beginning it might be hard for him to cast every Q it might be useful purchase
that later on becomes
, so you don' t have anymore mana problems, or start with a double
that later on becomes
The difference is the first one allows you to spam more, the second one adds magic resistance and if the enemy is a mage allows you to survive better if you get caught! . When you will be more experienced you can try other things like
and so on ^_^
When he hits 6 he is ready to massacre his enemies: start to get heavy AP equipment when you can, while fighting try to not expose too much yourself and try to weaken a bit the enemy with your other spells, then finish him with a Q+R combo!
You must pick fragile targets, check if they have magic resistance by pressing tab.
When your fingers will be more nimble you can do more numbers: you can cast E, Event orizon, with the border right under the feets of your enemies so you will force them to get stunned, cast W over them and Q and R soon after: the damage is HUGE and there are very few people that can survive.
Remember to not suicide yourself, and to not throw all your skills if the enemy has full HP bar else he might survive, but weaken him qith Q or W.
Use the W to clear your lane very fast and don' t let the enemy mage put down your turret first, but always keep your focus on farming the Q at all levels.
remember to get
if 2 or more people in the enemy team have magic resistance and to get
once you have at least 1 ap item and you have farmed a bit: the results are devastating, and about boots go for 
There it is soo much to tell, but i want to keep it to the basics: after you hang with him a bit you will understand better positioning, prediction, items to pick etc so i don' t want to teach you all in once! Good games!
I put here a set of items you might liek or not, without too much explanation: see if they fits your fancy!
