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Smartcast everything but your stun. You do this by going to the keyboard settings and changing QWER to Smartcast instead of regular cast. This will eliminate your need to mouseclick the spell in order to cast it.
Don't be afraid to spam your stun and dark matter to catch enemy champions. Make them fear your range; let them know you will kill them if they come close. Get into their mind.
Your stun can be a great initiation. Nothing is better than Veigar's initiate because you instantly make the team fight a 4v5.
Save your stun for when your jungler comes into the lane. Your stun plus your junglers damage will usually ensure you a kill.
When you use your stun, make sure to dark matter right after; even if you don't think it's going to hit. You should be using SMARTCAST and using both at the same time.
When creating a pick sometimes a better to cast your stun behind the target so it keep the enemy team from being able to help him and it also traps the target.
In the laning phase, hard harass at level 3 with your level 2 Q, like this you can create an opportunity to kill them at level 4 with the E/W/Q/Ignite combo.

Last hitting
Don't always last hit with Q! 10 or 20 ap is not that important Save Q to harass when the enemy champion is going to last hit. However make sure that you always save up your Q for a cannon minion, this will give you two AP instead of one!

Using your Combo to get kills
Your combo can literally one shot almost anything. Once your ultimate is up, just wait for the right moment and start snowballing off of kills. The combo order is to use your Stun first then use Dark Matter because there is a delay before Dark Matter hits the target. Follow it up with your Ultimate and your Q to finish up your Target.