Laning phase might be one of the more important component for Vel'Koz support. While you may use your W to poke, be aware of your mana in early level before getting any mana items such as Frostfang and Lost Chapter. Also keep in mind to refill your rejuvenation biscuit everytime you back (have around 1-3 biscuits in item slot). Try to be aggressive, but remember to always check river, since you do not have any mobility(yet). If enemy jungler/mid laner came to gank, use your E logically to cc them while you and your adc escape. Use ignite as a kill secure spell or use it along with your other skills to kill the enemy. Try to poke as much as possible to fulfill your 650G gold quest, which gives you movement speed and 15 Gold everytime you poke the enemy with your abilities.

Be aware to attend as many teamfights as possible. Try to use your WER combo in teamfights when enemy are close together. Proc thunderlords and your passive just like the laning phase. Keep in mind that in this phase you should be able to gain movement speed everytime you hit the enemy champion with an ability, so use your W ability when you are getting chased and enemy have a fair amount of distance to you. If they are extremely close, put down E and right after a W to escape quickly. If dealing with any assassins that have high mobility/untargetable etc such as Master Yi, try to place the E ability as close to you as possible (right beneath your character/around it but very close). This will maybe give you a chance to airborne them. Use your W right afterwards if you failed to stun the enemy.

You should be able to deal enough damage in late game. Switch some items into magic penetration items such as Liandry's Torment or Void Staff when enemy have magic resist. As long as you go along with your damage dealer (adc or mid), you can deal excessive amount of damage while being safe. You don't have to worry too much in late game since Vel'Koz late game is pretty strong, because not only it can deal a lot of damage with abilities, it can also proc true damage from his passive which the enemy cannot block it and it can deal tons of damage.