In the laning phase, Vel'koz likes to farm hard while slowly chipping away at the enemy's health bar. Trades are won by those extra Q's that land after the even trade occurred, or those W's that happen to pop with an enemy on them. Do not try to force trades when it sacrifices CS or puts you close to their turret. When trading with assassins, always keep in mind what times they could kill you at. The biggest tip about trading though is to NEVER UNDERESTIMATE WHAT YOUR OPPONENT CAN DO. ALWAYS give them the benefit of the doubt if you don't know if they could kill you or not. Your biggest goal is to not be useless. Feeding makes you useless.

As far as farming goes, you want to shoot for 70 cs at 10 minutes. Keep this up as the game goes on, although it should be easier after you have luden's echo. You want to shove your lane when your laner backs, and freeze in front of your tower at all other points. When they back, you can do one of two things: shove and recall, forcing them to miss cs to their tower, or you can roam bot or top. Roaming follows the same guidelines as fighting in lane. Never go too deep on Vel'koz.

Midgame, you are an excellent minion manipulator. You can clear waves in 1 waveclear combo (W-E-W) and force the enemy to defend their towers when you are already back on your way to the team for a 4v5 fight now. Additionally, you can get any champion to chase you and kite them to death or force them to base to miss teamfights. To kite people in this way, use your W while running to deal extra damage as it doesn't interrupt his walking, use your q to slow one or more enemies getting too close to you, and use E only if things go south and you need to get away NOW.

Your goal should be to take advantageous teamfights. I have detailed a few ways to set up these scenarios, but you just want to take fights where you are not in danger and your team has either a numbers or setup advantage. NEVER take a fair fight. Your goal should always be to get their nexus to explode, never to kill them wantonly. Once again, DON'T DIE as dying means you are not winning and every time you die is YOUR FAULT and YOURS alone.

Lategame, you are not to die a single time. Your pressure is unparalleled, and your siege potential is immense. Positioning is key to making this happen, so make sure you are always thinking about what situations you are putting yourself into by going to certain spots.

To finish the game smoothly, make sure you are using your team's frontline to be as effective as possible in teamfights. The protection that a tank can give you can double your effectiveness. Urge your team to do baron if it is safe, or to push a lane together. You are most effective in teamfights that are set up well, so make sure you are doing that.

If you lose lane, the most important thing is staying calm. You want to stem the bleeding and claw your way back into the game, so the first step is playing like a *****. Don't even get near fed enemies, make sure you have vision everywhere you go, and get every single minion that is available to you. If your laner roams, ping like hell and DO NOT FOLLOW. You get a 30-second to 1 minute interval to get as much lane creeps as possible in this time.

On Vel'koz, you die easily no matter how well you are doing, so your mindset on positioning should be normal. Just do not be aggressive when you are behind. Your chance to come back will come when you work with your team mates to gang up on single enemies or pairs of enemies. NEVER TAKE A FAIR FIGHT.

If it is later in the game, you will have limited chances to come back into the game. Your only options will be trying to work with your team to do baron, deathbush an enemy to create a 4v5, or something like that. You can't really poke them out like usual if you are extremely behind. These options are high risk high reward, so be very careful.

Combos:

Lane Solo Kill: Q-E-W-R or Q-W-E-R
Teamfight (multikill) E-W-R (Q stragglers with geometry)
Lane Trading Combo: Q-W-(can follow up with E-Q-W-Ignite)