This build is focused on farming through laning phase and be a tanky ap carry that can even initiate with a (potentially) five man stun. Try to avoid lane assasins and always ping when you laner is missing. Don't even go past half the lane if you dont have flash to avoid ganks because veigar has 0 built in moblity.
Try to farm until lvl 6 before you even try to fight and whenever you want to trade use you e, w then q and you can probably ult, q and ignite for the kill after.
In mid game try to use your glory with your whole team to start a teamfight and use your skills as much a possible kill the catched squishys and then try to kill the rest with your team and use your mana shield to stay alive. You will likely get a free dragon or tower(s) afterwards.
In late game you are the most annoying mage of the world because you will not die easy and always get a lot of damage done but don't forget your actives! Try to get good teamfights and burst the squishys (this is alway possible if you arent behind too much).
Btw this build is weak to %health damage from vayne or kog'maw because its doesn't have much room for armor.
PS:you can also go ghost + flash and build switness+distortion if you want even more movespeed

With veigar your early trades are really bad so try to avoid them by staying back and stunning your lane opponent whenevr he/she goes in.
The normal harass combo for veigar is: use e then w on top of him if he's stunned and then q him for good mesure. If you want to kill him use your ult before you q and then ignite but try to trade one time before you do this because this is not a dfg build.
Veigar usually likes to stay in lane but try to roam if you get the chance because you cant really stay in the middle of the lane safely.