Illaoi is a very strong top laner with tons of damage and good zone control. Personally, I believe there are basically two ways to build her according to whom you are up against. A more Tanky Illaoi or a more fighter Illaoi. All basic builds tell you to tank up but that is not always the case, the tentacles's life steal is a pretty good sustain when you activate your R.

The logic behind these spells: Flash is a must, not only to get away but to flash into the middle of a group of enemys and ULT right in the center. Ignite is in because usually champions tend to run away when Illaoi Ults and also to compensate for champions who use excessive life steal like Garen, Nasus, Swain, Atrox or Volibear.
Other options are "exhaust" or "teleport" to help out the bot lane.

What you have to understand is that Illaoi is very strong when within the tentacles' range so try to place them nicely along the outer wall and at the entrance of the river, the enemy will kill them but just keep putting more and never engage where are no tentacles. If you have to fight with no tentacles around try to rip out a soul (E) and combo a W,Q,autoattack and repeat.

Try to be annoying with the Q and W some minions to get the farm but don't force a fight before lvl 6. If the enemy champ is pushing for a fight its best to retreat until lvl 6.

If you are pushing in top lane and you get ganked, no worries, just get near a tentacle and try to reach either champion, preferably the jungle, with your E and then ULT (R) that usually gives you a double kill. If you miss that initial E, retreat! (try this at your own risk)

In late game or before the team fight, try to use E as much as possible and your team will help you kill the soul. That is a real pain for the other team in the moments before a team fitht. Remember that a Vessel spawn tentacles randomly so this is the moment to go on the offensive.
Be careful cause you are usually one of the fist ones in a team fight and ULT. Your worst scenario here is a stun or a silence. If so, flash out ASAP or just take the heat and let your team's ADC and mid do the damage.

At the end I have marked champions you should really watch out for. Most top laners respect Illaoi and will give her space being afraid of ther Q or tentacles, like Fiora or Mster Yi but some tanks might just be in your face all the time hogging the farm. It's best to push slowly with Q or E and avoid getting killed easily.

IF ILLAOI FALLS BEHIND FARMING OR FEEDS THE ENEMY...GG

Since Illaoi is at her best with the R, the build is aimed towards cooldown reduction. (this is my personal suggestion and will accept other ideas) :)

DISLCAIMER: I know that logic dictates that "your job is to tank up for the oncoming teamfight in late game". Yes, your role is to be the spearhead of the team in late game but this build also achieves that and feeds her pretty well.

This may sound crazy but ignore Doran blade and go straight for a common +10 dagger and a health potion and start building the Black Cleaver soon. It provides health and a 20% cooldown reduction. Your tentacles and your Q heal you on impact WITH A CHAMPION so you have pretty good sustain there. The potion is in case of emergencies early on. Once you build The Black Cleaver you have to make a decision. TANK or keep up the damage. That depends.
Do you feel like you are having problems taking too much damage? Go for the Frozen heart or Spirit Visage. Or do you feel lucky and want some kills? and build the Titanic Hydra or Sterak Gage (if you build it while still alive she will react to your purchase). It is very advisable that for a team fight you build at lest one MAGIC RESISTANCE item if there are AP enemy.

The logic: The frozen heart provides the highest armor AND 20% cooldown reduction. Black Cleaver and Frozen Heart cap the cooldown reduction and the R cools down in a little over a 70 seconds. The Q in over 8 seconds and the E in just over 10 in late game. This is paramount since all or almost all of her hits and attacks are ability based. If the spirit visage is not enough, top it off with a banshee's veils and/or Mercury's treads. The Randuil Omen is in case you are fighting champs that keep running away. People always forget that it ACTIVATES and SLOWS enemys around you for 60%. Very useful agains attack speed champions or skittish range champions.
The duskblade and Youmuu's Ghostblade give you armor penetration should the enemy tank be too...tanky. Like a Garen or a Malphite. These items are far from recommended and should be bought as a last item (I know the ADC should do the damage but you'd be surprised at how much killing Illaoi can when alone or in the middle of a team fight).

Whan against another Illaoi is all about who can control the area better. Place the tentacles carefully as you advance and kill hers. The first Illaoi that lands an E on the other will have the upper hand. Stay behind your minions and a little to one side to avoid the Q. Just farm, calm and chill. When at level 6 you have two options
1) engage Illaoi upfront tempting her to throw her R, then IMMEDIATELY back away to one of your tentacles and out of range. Try to land an E and you engage her there with your ult.
2) flash or W ner her and YOU ULT FIRST. If this doesn't happen do option 1.

The jungle should gank Illaoi as early as possible before lvl 6. And after that just poke her and tempt her to throw her R. Then retreat and tag team until it wears off. (in my experience full on AoE an Illaoi will get you killed).