Vel' Koz needs a lot of patience, in the laning phase it's more about trying to get a cs advantage. If you are constantly pushing forward you are incredibly immobile, you will die and you will lose lane. Gain a cs advantage, poke, and and don't feel bad about ulting to push someone out of lane. Once your in the team fighting stage you;ll have enough cooldown reduction and enough mana regeneration to constantly through out your spells (which will hopefully be slowing people with Ryalis Scepter). Once you ult, you will doing 35-60% of the entire enemy teams life (if there grouped). Try to stay on the back line, you have the range to not get in the middle of the fray. If you happen to be the last one alive on your team or you get caught out in team fight phase run backwards and throw out slows and knock ups and your damage, your spells are designed to to damage to people who chase you.

Pro's
-Good damage
-True damage
-A large amount of slow (with Rylais)
-High amount of group damage
-Can kite very well (with Rylais)
-Most spells go through minions
-Excels with front line tanks.
-Long range

Con's
-Highly immobile
-Not much health
-Item dependent
-Mana dependent
-Has a few strong counters
-Almost everything is skill shot