Fiora is a TANK DESTROYER. Well actually she is fair and treats everyone equal, no matter how fat he is and how much armor and magic resistance he has, since her damage is... true and depends on max HP.

Your whole game will work about her passive, hitting Vitals. Only with that she can deal that wonderful true damage noone can handle - you better learn to hit those Vitals versus Bots first, if you never ever played new Fiora.

What you have to know first, before you charge into battle - she is a lategame carry. So in her early game she may lack some damage compared to some heroes. Only thing she can do, is to hit a vital and run away before she takes too much damage.
You are pretty squishy and since your % damage scales with your bonus AD, as long as you have none you won't be able to do any real significant damage.
That's why you shall focus on getting faster to the such desired lategame.
Of course you can and you shall win trades early on to get a dominant position on your lane so your lategame will become much earlier.
So the main thing you should to, is to hit Vitals. All those speed and CDR thingies you get are there so you will be able to hit vitals faster.

How does it work?

After you hit Vital, you will heal a little, get faster for a short time and proc all onhit effects.

Your Q, your W and your autoattacks proc your Vitals (also your E). Your Q also procs on hit effects like life steal or slow and your Black-Cleaver passives. Also the cooldown is greatly reduced when you hit something with your Q. Use it on minions to chase someone down or to escape. Important: THIS SKILL WON'T PROC YOUR GRASP. This means you still have to autoattack afterwards to steal health, remember it while trading with someone.
Learn about the range of your Q. Its big enough to hit someone but not big enough to hit someone's Vital from behind. You need to be nearly in melee range to be able to jump behind your target and proc your passive.
Your E resets attack timer. use it direcly after you hit someone, so you will hit twice and slow him down.

Your W makes you immune from any damage and CC for that duration and if you catch a spell you will throw it back. If it was a stun, the enemy will be stunned, which is very strong if timed properly (especially on champions with 1 "big" spell which you just block away, like Veigar's ult for example). Some of spells go instantly and you have to predict.

Your ult makes you faster near your enemy and marks 4 Vitals from all sides. Its hard to hit them all, that's why we take that Mastery talent and all those items like Black Cleaver and 45% CDR cap.

How you shall use your ult properly?

You will want to try to hit 1 Vital and then use your ult directly to do as much damage as possible in short time. But in most situations that will be pretty hard to realize, so don't hesitate to start directly with your ult. Try to get in the range normally,pop your ult (remember, when enemy sees that he has been marked, he will try to run away in most cases) slowing directly your enemy with your E down while proccing the first, nearest Vital - after that you use your Q to hit instantly second Vital. Try to land your Q behind your opponent - in direction he want to run away, or in direction where is the nearest wall so he won't be able to hide his spot from you prevending to proc your heal.

With 40% CDR you will be able to use your Q faster and proc Vitals faster (your movement speed won't be enough in most cases) and kill your enemy faster.

Mostly you will have a hard time before you will get some levels and core items. Depending on your opponent, you will try to freeze the lane near turret (especially vs bullies like Pantheon, Yorick). You will try to trade a little by hitting them with Q and E on their vitals and run away before they can react - but if you miss and get caught, you are pretty much dead. Also even if you are mobile, don't overextend, since you can always be ganked.

Don't push the lane except one situation (later). You don't want to get ganked if you overextend or let your enemy farm (even under turret). Your main job early is to harass and farm, and farm is more important, since the faster you will get into late, the faster you will win.

Your perfect scenario: You harass your opponent so hard he can't trade with you anyomore and runs away from you. Instead of overextending and trying to towerdive you can do following thing:

1). Freeze lane
2). Stand between your enemy and his minions

This is called zoning. He can't farm and if you zone him pretty hard, he also won't get exp. This will give you a large advantage. Be prepared to be ganked, that's why you try to freeze near your tower.

When you shall push:

1). If you have more minions than him. Like double minion wave for example - it is better to bring them faster to the opponent's tower and deny with that his lasthits than letting him get all of them (but it won't always work, some people are good at lasthitting under turret, just like you)

2). If your opponent has backported. If you push properly and backport after you kill the siege minion, when you get back to your lane your enemy will have double minion wave, which is good for you, since you won't miss much farm.

It may sound obvious, but your target is *obviously* the enemie's AP or AD carry, but in most cases you won't be able to reach him without taking fatal damage.

So how do you deal with it?

With that build you are pretty much tanky. You still deal decent amount of damage on EVERYONE withhout being oneshotted by someone. That allows you to kill other people to clear the path to enemie's carry.

So in most cases your main target for ult will be... yes, the fattest guy of the enemy team. That one who is always in front of everyone and who thinks he can just charge reckless in while his team follows up after some time. What a stupid thought while playing vs Fiora...

Since those tanks/bruisers won't be hiding somewhere behind and are easy to reach, and are in most cases pretty slow without real escapes (they can charge in, but not out!) you will be able to deal really significant damage to shut them down before the enemy team can follow up.

With that build your ult will deal around of 50% of his max hp (only damage from your 4 Vitals, you also will deal some damage with spells/autoattacks!). If you proc a Vital after that, and your team also does something he will be dead in like 2-3 seconds if it works perfectly, and up to 5 seconds if not. And after that that big heal comes and you can still kill the carry afterwards.

The idea behind it is to make as much damage with your ult as possible, and since your ult does % true damage the best target for it would be a tank. Of course it is also very useful on a carry to kill them even faster, but you won't be able to do it if they play well.

By killing their tank without losing anyone (except your ult CD) you will be able to win teamfights with ease.

Overall this guide seems pretty finished. I will update design and add some matchups