Code: Fizzlesticks.

Seriously, if you play as Fizz, no Fiddlesticks will attempt to confront you in a 1vs1.
His W, Bountiful Harvest, is completely useless, if you counter it with your W, Seastone Trident.
Fizz's E ability, Playful / Trickster also allows you do dodge any ability, auto-attack, whatsoever.

If you don't own Fizz, or just don't like playing as Fizz, follow the advices others already mentioned:
Grab Ignite as summoner spell or simply buy Executioner's Calling.

Fidle isn't OP, but wards are. Just start with boots + 1 ward and go ward his blue and gank him when he does it. Fidle can't jungle without blue. If you manage to steal his blue, ward yours, because HE IS going to do it.

If you want to counter his ult, once again, OP wards are there for ya.

If you want to counter the 10 hours long fear, get QSS

Its all about kiting him, and making sure he pays when he drains in lane. Don't let him combo you, and make sure you have atleast some merc treads or a QSS. The channels can be interupted, get someone to do that. If you cannot 1v1 him, DONT! He is very fragile, but dominates 1v1!

Also, like said above, Ignite or Executioner's Calling (If your melee) helps LOADS.

If you interrupt his drain he dies quickly unless his ult is going

Nope.

He's definitely not OP.
Counter him early. Gank him at blue buff, make sure he doesn't get it.
Ward positions (bushes etc.) from where he might ult and either interrupt it or back off when he does. Alternatively, you can blow him up right after his ultimate if your team's focus is good, but watch out for him using Zhonya's Hourglass.

Also, Ignite helps.