How do I handle Fizz as being Velkoz?

Stay as far back as possible. Your Q and W have pretty crazy ranges, and if you can keep your distance and make him push towards you you can sit relatively safe under your tower and force him to blow some of his burst combo just to reach you, which helps you survive.

Lane wise, I would only use your stun after baiting out his E. I would build something with HP/AP first before getting Zhonyas, that way you won't be taken down so easily.

Don't pick Vel into Fizz, and first picking him is risky in general.

If you are stuck with that matchup get and use it if he hits his ult, but always try to dodge it and stay far away.

If he hits it when you don't have Stopwatch (anymore) u probably ded, even under tower if he doesn't fuck up. Flashing in the right moment might safe you too tho, but don't rely on it. Oh and I would take as second summoner to survive the burst.

Your job is basically to just farm the lane phase and not int, don't try to ever take lane prio or go aggressive after level 3 if he didn't fuck up heavily and you are 100% sure you get the kill, and always try to set up some river vision when you can for your team as he will try to roam because you play passive.

Fizz hard counters Vel'koz AND Fizz is doing quite well at the moment, so I'd ban him if possible.

Pre-6, bully him as much as possible with Q and W but always keep at least one charge of W and don't use your E to poke him unless he's playing super passive for whatever reason. If he does try to jump on you, wait until he leaves his E to use your E on him + the W you saved to proc your passive and hopefully even out the trade.

Post-6 is hard. Since you're Vel'koz, you're probably playing as far back as possible but if you get tagged with his max ranged R you're probably dead. I'd focus on farming and (hopefully) beating him in team fights. Perhaps take the Stopwatch rune so you have at least one way to survive Fizz's engage past level 10. Banshee's Veil can help too if he forgoes Protobelt to pop it before he tries to land R. Zhonya's will undoubtedly be essential later on in the game against some AD threat on the enemy team but is again useful against Fizz Ult too, so buying it as a third or fourth item is almost always a good idea. Of course, he can viably build both Banshee's and Zhonya's to make it even harder on Vel'koz though.

Barrier summs with Flash.

You can try to bully him in the first 3 levels, after that, just play defensive and only trade when you land a good QE.

Assuming the Fizz isn't new, you'd spend most of the time trying to freeze the wave at your turret until jungle comes to gank for you to unleash your wrath.

CS from Q and W only from as far as possible until you hit 6 and above. Good anticipation is key (Vel's bread and butter). It's not easy since he can escape your R pretty easily and you're basically too vulnerable during ult.

you don't. he is your hardest counter. use your cc where he's going to be.