When in lane you want to be sure you are getting your last hitting done on minions if you are in a role other than support. You can poke from a distance with your Q. Keep in mind that you can recast your Q after you cast it to shorten the distance that it travels before it splits. The ideal combo for Vel'Koz is E, W, Q, W, R. If done right mid to late game pretty much will guarantee that you take out the champion you are fighting.

Keep in mind that you are very squishy and you have to stay behind the front line or make sure that you have someone on your team that can peel well for you. If an assassin gets to you, you're done. If you get into a situation where an enemy is chasing you you should be able to kite them well with landing Q's and W's until they are low enough (and dumb enough) to keep chasing you and you can kill them.

Be sure to fire your Q in many different directions to include over walls and what might look like out of bounds for the enemy as long as you can hit them with the perpendicular bolt that shoots out when it hits its max range or you recast to shorten the explosion usually catching them off guard most of the time.

When you choose to take Vel'Koz bot lane as a support character you should be able to easily out poke your opposing lane. The max range on Q is very long and you can make sure to use the angles to get around minions and hit the enemy ADC/APC or support. There are not many supports that really give you much of a threat when you are playing as a support you have to be sure that you dont get caught out for easy kills or get caught by roots such as Lux and Morgana have.

Be sure to save your E for kill securing or assisting the jungler when they come to lane for ganks. If you can land your E this will almost always get them to burn heal or flash (or both) to get out of the gank and live. You should use your ignite early in a fight as well so that you dont accidentally take a kill that could go to your lane carry as that 300 gold (or less) can be detrimental to them later in the game if they dont get it early on which would put them behind.

YOu want to make sure that you use your Q as often as possible, spam it almost. You dont have to hit every shot but make the enemy be concerned about the fact that it could come at them from any direction any time. Vel'Koz is a very good 1 on 1 champion and will win most matchups against other mages. As mentioned in the threats you want to make sure that you do not allow any champions with gap closers to get on you because if you do you will most likely not survive.
You're Ultimate is on a relatively short coold down so you should be using it often, even if its just to clear a wave of minions or take 1/4 to 1/2 of the enemies health off quickly to possibly force them to back.