I just started playing with Fizz and as an Ahri Player I really wonder how you sustain with Fizz on the lane (or at all)? He hasnt any Build-In Spellvamp and also no AP Build foresees someting like Hextech Revolver for him. Don't get me wrong - I am not like "oh my god I can only buy according to my build" but there must be a reason you don't build something like spellvamp on him. I mean I really have a hard time to hold the lane when I get harrassed...So my question is - How to sustain with Fizz? Maybe to give some kind of half answer - does it all depend on evading harrass with my E ?
The key to midding fizz is, as someone already mentioned, managing trades to get a pressure lead early on.
I like to think of it in these terms. In starcraft 2, it is commonly said that to win with zerg, as a general rule, you should always have one more expansion than your opponent, and you do this by expanding early.
With fizz, begin initiating trades as early as level 2, and maintain a health advantage by constantly diving in for trades as your counterpart approaches the wave to last hit.
For the trades, as they approach the wave, dash in with Q. As you land, activate W before your first attack lands. Auto attack them twice, maybe three times if you can get away with it, then E to get out.
Usually once you Q to them, they either start to panic and don't cast anything, or show absolutely no sign of worry and start throwing spells out. Just juke a bit between auto attacks if they don't instantly back off, which will put them in an even worse position, and tilts the trade even more in your favor.
As you E away, occasionally they will try to even out the trade a bit and throw a spell out, if that is the case, you can elect to use the second half of your E to go back to them and apply more pressure, as they just wasted a cooldown.
After 6 it doesn't get much more complicated, just add the ulti into the rotation wherever you see fit.
Of course, the usual laws of midding in general apply, after you do it multiple times, you can get predictable. Be aware that while your E does make escape pretty easy, if baited into a situation just that little bit too risky, it can be fatal. Remain aware of how your lane counterpart changes in behavior from level one onward.
Other than that, make sure to get your farm in whenever you aren't harassing.
You could say that it isn't really "sustaining", but ensuring that your counterpart is even less sustainable than you are. If done correctly, they aren't even "trades" really, because often times you will take no damage other than some auto attacks.
Hope this helps, and sorry for the large response.
Fizz, as a Champion, is incredibly different from most other APs that you would take mid. His skill set is the definition of high risk, high reward. If you can master Playful/Trickster, landing Chum The Waters, and using Urchin Strike not only to get in, but to get out as well, then you will become a very good Fizz player.
While buying Spell Vamp might seem worth it on Fizz, from my own experiences, it really doesn't help much.
You can rush a catalyst for sustain later. However, fizz isn't really that great early against lanes with sustain.
I see fizz having a lot of strength in his ability to initiate and control trades. If someone like an oriana tries to harass you with a q, initiate a trade because she just blew some of her damage and if you dodge it, you'll win the trade for sure. I personally think fizz is situational for non sustain lanes where his initiation/trading is highly in his favor.
Fizz is really easy to use if you get the flask and some health potions. I easily out-sustain even a Twisted Fate with full health pots and a flask. That being said, somethings to watch out for are pushing for that tower dive kill, while backup arrives. It's very easy to trade with Fizz and one low health champ can easily become two. Jungles thrive on baiting the mid laner to their own turret and charging them. A good Hecarim can totally mess up your mid lane even if you outpace your enemy. It's a very good idea to ward when you go mid.
the main reason why you don't go spell vamp on fizz is because he is a burst class assassin not a constant damage dealer like katarina (kat has very less cool down on her skills so its worth buying spell vamp on her)but with fizz you are going to focus one or two people and flank them from the sides
early you feel like you dont have sustenance but once you max out your playfull/trickster you are a monster you have an inbuilt zhoniya's hourglass in your package with a added flash why you need sustenance
your playful/trickster is a very strong disengage if used properly i would suggest to buy cool down reduction items than others.
laning against certain champions will be more difficult like leblanc, mordikeiser,yasuo,vladmir, etc
the key is take advantage of their cool down time to trade damage also try to cs without using skill in the lane and force the opponent to use skills to cs which will give you good results