Fiora is an amazing AD carry who focuses on longevity and quick attacks. Her passive ability keeps her Health Regeneration rate up as long as she is attacking, and increases as you attack champions. Fiora makes a great solo character as she has good perseverance, decent escape ability, and quick burst damage.

You want to focus on dealing damage with your rune build, but you also need a bit of survivability. All of her attacks are physical in nature (with the exception of the reflection of damage with Riposte) and proc all on-hit attacks (like Lifesteal, Slows, Armor Debuffs, etc).

Armor Penetration Marks will help with your early game damage by making sure that your damage gets through with as much efficiency as possible.

Resilience Seals will help you stay alive enough to stack your 4 passives against a champ, get that extra attack that takes them down, or lets you run away long enough to live.

Crit Damage Glyphs will help you get the most for your attacks by ensuring that those crits are big (healing you more and killing them faster).

Finally, Per Level Attack Damage quints will give you that late game burst damage (and burst Life Steal healing) that you need to really take out the other team in team fights.

It's pretty straight forward. Just like your runes, you want to have a balance of damage and survivability. However, late game your damage is your survivability by means of Life Steal. As such you should max out your Direct AD damage and then dump the rest into Armor and Health.

For your items you really need to focus on attack speed and attack damage early, and life steal later. Bonus health, armor, or other effects are good but should not be your focus.

I always start with my attack speed dagger and immediately build toward Berserker's Greaves. This will give you the speed boost and attack speed that you need to gain an edge on your opponents. After this, build your Wriggle's Lantern. This is an all around good item as it provides some health, attack damage, and life steal. It also allows you to put up a ward periodically to either guard against Ganks, watch the Jungle for a quick gank, or simply to keep an eye on things somewhere.

Next, build your Phantom Dancer for more attack and movement speed, and to start building your crit chance. Once you have these three, you have some options, but you want to continually increase your attack damage.

I start with Bloodthirster to increaese my survivability and damage (also has a stack per kill effect). Next I build my Black Cleaver which maxes out my 2.5 attack speed when using Burst of Speed, and rips down their armor as it goes. Finally, I pick up an Infinity Edge to complete the build. This item increases your crit chance, damage, and makes your crits do 250% of damage (plus your +crit damage from runes). You will be striking 2.5 times per second during Burst of Speed at 55% crit chance... you will be doing a lot of crits.

If your game is dragging on, or your opponents seem to be running a lot (you have high movement speed opponents), building a Frozen Mallet will stop them in their tracks, allowing you to really chase them down. However you will need to drop another item

There seems to be benefits to taking Lunge first, it allows you to close the gap and do damage, but without some way to survive in close this is almost always suicidal. I choose to start with Burst of Speed first, which once you strike gives you increased attack and movement speed (allowing you to kill them fast, or run away if you need to). I max this first since this is your primary means of damage increase, and once you have some life steal this will help you recoup your life quickly.

Second I take Lunge, this allows you to close the distance and start your Burst of speed. However, the damage output is minimal and it serves this purpose (closing the gap) just as well with one point as it does with five. Because of this I take a point at level 2, and then max it last.

Third I take Riposte. This is an ability that has a passive benefit and an active ability. When activated the next basic attack (or ability that scales on attack damage) is reflected back. This also cancels out any effects that hit applies. This is critical as it allows you to reflect Gangplank's Parlay, Shaco's Two-Shiv Poison, and similar abilities. If you are up against a Champ who makes significant use of these kinds of abilities you may want to take this first instead of Burst of Speed, but generally you will level to 3 fast enough where that won't matter. Because this has a passive benefit and can save your life in a pinch I max this second (dumping a point into it any time I can't dump into Burst of Speed or Blade Waltz

At level 6, 11, and 16 make sure you are leveling your Ultimate. Fiora's ultimate serves as not only a great offensive attack, but has amazing defensive capabilities as well. When activated Fiora will fly around attacking any enemies in range. She will always start and end with the enemy you targeted. Each hit deals damage and activates on hit effects, so in a team fight you could rend armor, slow attack speed, or apply other effects to the entire opposing team. At the same time this activates her passive (increasing your passive health regen, stacking up to 4 times for each champ hit), and activates life steal. In addition to all of this it makes you untargetable (by towers and AOE as well), so it is a great way to regain life and force them to attack another player.

In general the way that I attack would be to lunge in for a quick strike, activate Riposte and back out. As they chase you they will reflect the damage of their first attack back on themselves. Next, activate Burst of Speed and use the second proc of Lunge to get back in. Typically they will be running away at this point, if not stand and fight. If they are fleeing and get out of melee range you can hit them with Blade Waltz to do some more damage and close the gap again, if they stand and fight and you start to get low on health hit Blade Waltz to keep doing damage, regenerate health, and disrupt their attack (this is especially helpful against Champs that are using AOE, and also against Trynd when he has activated his Ult and is running away).

I always take Flash or Ghost, along with Ignite. Flash and Ghost are great because they allow you to close the distance faster and begin your attack. They also allow you to escape with yoru life in many situations.

Ignite is great because you can target and use while you are in Blade Waltz, so while you may not kill them with that ult the Ignite might finish them off. In addition you can Lunge in, hit ignite, and then back out.