hello, my name is tomashock and this is my first guide here on mobafire (and elsewere) so i'll try to do my best. English is not my main language so be nice.
Nautilus is mostly played as a tank, health tank due to his w shield which scales on hp. The huge amount of cc this champ has makes him very usefull in teamfights, chasing and protecting your carries, this is why he is so versatile and can be played as jungler, support but mainly solo top champ.
Why AP/TANKY solo top? well, even if his spells dont scale very well with AP, every time u dredge someone, and u spam ur combo you will notice the huge amount of damage you can deal. Also, ur passive and spells allow u to farm like a boss while keeping a good harassment over ur enemy laner.

This is a long guide, i know. Be sure to vote after reading and trying the build, there are a lot of shorter good guides around, but i think every different build has a different gameplay so i will try to explain every detail of this champion.

Pros

- Heavy cc champ
- if ignored you can disrupt their entire team
- nice sustain with shield
- when mastered, easy farming
- nice initiator
- you are almost as big as a turret

Cons

- can be ganked easy without map awareness
- very slow attack speed/movement speed and hard to master attack animation
- doesn't scale very good on AP
- depends on a skill shot ( Dredge Line) to initiate propperly

Your runes choice make the difference between a good top, and loosing the turret minute 10 with a pretty bad cs.
It is very important that u can hold the lane vs strong champs (like garen, jax, morderkaiser, nasus), that u can farm ignoring their harrasment, and that u can harras them as well. The runes i pick are mostly for blind pick games, when you have no idea who u are laning against, or if u are laning vs 1 or 2 pple. BUT if u are playing ranked, make sure to have 3 rune pages ready: full armor seals and glyphs (vs full ad champs like garen, wukong, nasus), full MR seals and glyphs (vs full mages like galio, vladimir) or hybrid defense for hibrid champs like kayle or jax.
note: runes are optional. U can also pick some HP runes to max your shield, but Nautilus is a very powerfull early game champ, and with full build, ur HP will rise to the top.

only a few comments about the masteries:

1. again, if You know who you are laning against be sure to max Hardiness/resistance and leave only 1 point on the other masterie.

2. Movement speed masteries (above 70% health) is not a MUST. Why? because ur combo depends on landing Dredge, if u catch a guy, u wont have to move to unleash your combo.

3. no mana masteries/runes: If u play well, and last hit you wont need a lot of mana to lane. The only times you will run out of mana are when your jungler arrives and you unleash the whole combo plus ignite plus exhaust OR when you are scaping an enemy gank (when u have to use all ur cc to scape, even your ulti) OR when u want to push a lane to go B (in which case u can just spam ur skills)

REMEMBRE: DO NOT USE YOUR SKILLS TO FARM IF U ARE NOT GOING B AFTER OR THE ENEMY CHAMP IS PUSHING THE WAVES TO YOUR TURRETS, DONT BE LAZY AND LAST HIT!

I begin the game with a Regrowth Pendant and a Health Potion,
if you have to lane vs 2 strong ad then go Cloth Armor and 5 Health Potion
then i try to get, AT LEAST, the philosopher's stone and 2 sight ward in my first way b.
[*] why 2 sight wards? simple. As a good solo top, you can stay in lane and farm as long as you have vision! Top is the easiest lane to gank, if your enemy is last hitting and the lane is even, there is a long way back to your turret if you want to run from a gank, make sure you not only ward the river bush, ward THE RIVER for 2 reasons:
1. you can see the jungler before he enters the bush
2. you can warn mid if you see the enemy jungler walking down the river
after that try to stay in lane enough to get a Giant's Belt. if you cant hold the lane, just buy whatever you need to counter your enemy laner, sticking to the build!
If the enemy is a strong caster, get a Negatron Cloak to ignore his harassment while you farm, if he is a strong ad, get a Chain Vest.
If you still can't hold, Call your jungler! This game is not about the killing, it's about the farming. just make sure your build let you do that, and you will be a late game monster.

Warmog's Armor: nice item if you are farming like a god.
Banshee's Veil: a must vs a strong ap team, decent health/mana and that spell block makes the difference between a good initiation or a stupid one.
Guardian Angel: the most important thing about this item is how fast you loose the enemy focus. "why killing a guy who can respawn".
Force of Nature: remember you will be building a lot of HP and their carries might want to rush madred's. This will mitigate the magical damage from madres's and will give u a speed boost.

Staggering Blow
A very powerfull passive. this is your farming and fighting tool
remember you can't use this twice on the same target for 12 seconds, you are not Udyr, BUT using this well allows you to farm the whole lane, even at your turret (see the creeping chapter)
in team fights you will be in the middle of the fight, surrounded by everyone, if they are smart, they will try to ignore you to get to your carries who, if smart, will be behind you. what you have to do is hit every enemy champ once to max ur passive's potential. you will win at least 5 seconds of no damage for your team.

Dredge Line
this is your initiation tool. do not engage until you have a clear shot, remember you can hit minions and terrain so, if you miss just go b and keep farming until its CD is over.
please don't try to grab people through walls, you are not Blitzcrank.
It's also your only scaping tool. you can scape a gank, or move faster spiderman's stile. just make sure you hit the wall...

Titan's Wrath
This is your main spell, max this first EVERY SINGLE GAME, the shield scales on HP and gives you AoE damage over time, A LOT OF AOE DAMAGE over time. this skill sinergises very well with your passive, if you manage to hit every enemy champion at least once (unleashing all your combo in the teamfight) you will be dealing a lot of damage to all of them every second.
this is also a farm skill (see creeping chapter)


Riptide
Your main utility spell. not a lot of damage, but a nice slow and AoE. It sinergizes well with rylai's cristal scepter and when maxed, you can clear minion waves easy.
also, when an enemy champ is scaping after the Dredge Line / Staggering Blow combo, they wont go 2 far after you spam Riptide, they will flash almost every time!

Depth Charge
this skill is AWESOME. It cant be dodged and, if used well, can hit every enemy champ on the way. You can initiate with this, finish off someone with this, or scape with this. AWESOME ULTI IS AWESOME.

So, now that we have the skill knowledge, lets see the skill sequences:
Harrasment 1: Dredge Line / Titan's Wrath / autoattack / Riptide / autoattack

Harrasment 2: Titan's Wrath / autoattack / Riptide / autoattack / Dredge Line / autoattack

Harrasment 3: Titan's Wrath / last hit minions next to your enemy (damage over time to surrounding enemies)

killing with your jungler: when your jungler appears, just dont be afraid to pop Depth Charge immediatly, then position yourself to Dredge Line / Titan's Wrath / autoattack / Exhaust Ignite / Riptide / autoattack

killing on your own: this only happens when you are too farmed or next to turret, wait for the enemy minion wave to be almost dead and if you are lucky your cc will keep the enemy champ into the turret's range long enough to die. just Dredge Line the enemy champ closer to the turret / Riptide to finish off the enemy wave (so he is the only turret target) / Exhaust Ignite / Titan's Wrath / autoattack / Depth Charge / chase chase chase KILL.

scaping like a boss: if they gank you, or turret dive you this is the way to go
Titan's Wrath / autoattack the one with more cc / Riptide for the slow / RUN like a boss! / this is the most important part, when you run, the guy you didnt stun will be chasing you and the other one will be left behind SO you have to use Depth Charge on the one left behind so you can hit both of them! / Dredge Line the wall/terrain / shift + enter "try harder"

Ok, imo this is the most important part of the build, every other aspect of the gameplay may change, but farming is your goal. Not only for nautilus but for every champ in the game.

Being a tank, with a shield allows you to walk into the minion wave and farm, also your passive gives you bonus attack damage so you sholdn't be missing any last hit.

If the other guy's harrasment is just too strong, or if you are laning versus 2 champions, just wait for the minion wave to be next to turret.

Remember this!!
1. full health melle minion, wait for 2 turret autoattack then last hit

2. full health range minion, hit, one turret autoattack, last hit

3. siege minion wait for the turret to do all the damage, then last hit. while the turret is focusing the siege minion, hit all the range minions once, so you wont have any troubles last hiting them. REMEMBER YOUR ATTACK SPEED SUCKS!

4. do not be affraid to use ur spells to farm a wave at your turret. The most important thing is to farm, if your enemy pushes the lane, and you last hit only, 2 things happen: there will be a moment when you will be farming safetly close to your turret without your turret taking out the creeps AND your enemy laner will be outpositioned. just keep farming untill your jungler arrives.

5. the best way to kill the entire wave without last hitting is Riptide / Titan's Wrath / autoattack once every ranged minion / autoattack once every melee minion.

6. EARLY GAME, NEVER EVER PUSH YOUR LANE IF YOU DONT WANT TO GO B! NEVER!!!!!!!! PLEASE, REMEMBER THE 2 THINGS THAT HAPPEN, YOU WILL HAVE YOUR ENEMY FARMING NEXT TO HIS TURRET, AND YOU WILL BE OUTPOSITIONED! JUST DONT. IF YOU WANT TO GO B, CLEAR THE CLOSEST WAVE PLUS THE INCOMING WAVE, THEN B. this will give you enough time to buy, and run to your lane without loosing much XP or gold! (sorry caps)

7. if you are having troubles farming next to turret, remember you have a shield. So use it and stop the wave before they reach turret range, wait for your wave to arrive, and last hit them.

I like Exhaust for 2 reasons:
1. even if your ad carry has exhaust, in teamfights the only one close enough to land exhaust on enemy carry is you!
2. you become the CC king

Ignite is optional, if they have a sion, fiddles, or any strong health regen champ, just waith for them to pop the health regen skill and ignite them. Also, its a good way to finish pple off...

OPTIONAL SUMMONERS

1. Teleport allows you to go B more often, gank bot lane when warded and most of all: dragon control. your team wards the drag, then you appear.

2. Flash when you think you will need more scape abilities other than your dredge, or may be used to position yourself for a good Dredge Line

3. Clairvoyance if you are support and you want to track their enemy jungler. never as solo top

4. Cleanse versus a heavy cc team.

5. Ghost if you feel slow, but remember why we didn't use the speed masteries...

Well, this is it. This is how i play this guy, and have very very good results. Just remember a few important things every game:

1. team composition is very important, just play something else if Nautilus doesnt fit the team
2. never follow a guide blindly, every aspect of the game is situational.
3. do not engage unless you know what you are doing. again, LoL is not about the killing, but about the FARMING
4. being a tank doesnt mean dying every time. if you sacrifice yourself to save a carry, good job. But if you are 0/10/x, no matter what your role is, you are sucking
5. Vote and comment after you have at least read the guide.
6. Thx for your time. I hope this helps you.