Will start to apologize for my english, i'm sorry but will try my best:)

This guide will just be a simple Nautilus walkthrough, won't present any advanced math for cooldowns, damage output etc. Will more or less focus on what I have experienced.

Nautilus have a lot of gamebreaking spells, such as his Q (the hook), his ulti, and my favorite his passive.

His hook as a great engage ability, in combination with the AoE slow and passive he can lock down almost any target. The hook is something a Nautilus player really depends on.
You'll need to remember that his hook can't go through walls, towers etc. And will on move the target 50% of the distance between you.

His passive is a unique passive, your autohit will stun the target for 0.5/0.75/1 second. This effect can only occur once every 12 seconds at the same target, this means 1 hit on each enemy will stun the team for 5 seconds together. Which will make it hard for the enemies.

The ultimate will follow the target where he/she goes, untill it's get there, and will also knock up every enemy/creep on it way. This spell works really good as a engage, disengage and for saving allies.

Nautilus is almost always junglin, and I can't see any role for him. He's not the fastest jungler nor highest damage output, but for sure the heaviest CC. As Nautilus you will need to try gank always, since you have this heavy CC you will always get at least some summoners burned from enemies.

When I say NEVER build for damage I really mean NEVER. Nautilus depends on sustaining in fights and just stop the enemy from moving around. Either you play a deffensive role and protecting the carries, but to do this your team needs to have someone else to engage a lock their carries. I prefer to play offensive in team fights, since Nautlius alone can lock once carry of the fight for like 6 seconds.

Pros:
Heavy CC
Good sustain in fights
Great engage and disengage
Eairly Nautilus can 1v1 many champions without even loosing HP

Cons:
He's not the fastest jungler
Low damage
Pretty slow (that's why u pick boots of mobillity)

• Greater Mark of Magic Penetration: These runes are a perfect chioce for Nautlius in the jungle. The extra Magic penetration helps with clearing camps faster, and allows Nautilus have that extra damage for eairly ganks. Alternative choice would be Greater Mark of Hybrid Penetration, which will boost your auto hits too. But i prefer to stick with the Magic penetration.
  
• Greater Seal of Armor: Extra Armor is something you really want with Nautlius, since he have low base armor(16 armor), you will need to get at least over 40. The armor boost really helps you sustaine in the jungle. I do have tried different runes in this slot, but without this bonus armor too much HP is lost.
  
• Greater Glyph of Armor: Samething here as with the Greater Seal of Armor. But this slot do have alternatives such as Greater Glyph of Scaling Magic Resist, these won't help so much in the jungle part. But against a more AP heavy team these are very effective.
  
• Greater Quintessence of Ability Power: The bonus AP gives you a nice boost in the jungle, since all of Nautilus spells stacks with AP. Also this will let you have a nice eairly damage while ganking. At this slot there one common alternatives the Greater Quintessence of Monement Speed, This are a very common quint for low Movement Speed junglers, and a very good one. So at this piont you must try out what you prefer.

Sorcery: With 4 points here you get 4% cooldown reductions. Since Nautilus have awful long cooldown on all of his spells, this will give you an extra boost.

Summoner's Resolve : Sure it's only 10g per smite. But in a 40 min long game you will have plenty of time for using smite, and then extra cash could be the difference between win and loose.

Durability : Sure 108 bonus HP at level 18 aren't that much. But the reason for this masterie is what you can pick after it.

Tough Skin : Reduce damage taken from monsters by 2, every hit. This aren't that much either. But also here we will aim for what comes after.

Hardiness : 5+ armor. This bonus will help you eairly in the jungle and of course while ganking.
This in combination with the reduced damage take from monster, will give you a much better eairly sustain in the jungle.

Tough Skin -> Bladed Armor : Deals 6 damage to any enemy monster that attacks you. This is included neutral jungle monsters, so also this will help my with the eairly jungle clearing.

Relentless : Reduces the effectivness of slows by 15%. This masterie makes it easier to gank, since if you aren't slowed the enemies will get caught by you. It will also help escaping, it's kinda obviously how.

Durability -> Veteran's Scars : 30+ HP, just flat not by level or anything. This means 30+ HP at level 1. This masterie is great for the sustain. Together with the combination of the rest of the bonus armor and reduced damage taken.

Tenacious : Reduces the duration of crowd control effects by 15% (stacks with tenacity). Also this will help you with ganks and escape. And since you aim to get boots of mobillity you will lack of the tenacity.

Wanderer : Grants 2% increased movement speed when out of combat. In other words you'll move faster between jungle camps, and also you get faster to the lane you wanna gank.

Meditation : +3 Mana Regen per 5 seconds. Since Nautilus often are a little short on mana eairly this masterie will boost the Mana Regen, and help you use abilitys in the jungle and while ganking.

Mastermind : Reduce the cooldown of Summoner Spells by 7%. Will let you use smite more often. I seen to often junglers who never have smite up while they wanna go for dragon or Nashor.

Runic Affinity : Increases the duration of every monster given buff by 20%. In other words Blue-/Red-/Nashor-buff will help you much longer. This might be the most important masterie for a jungler.

A must for almost any jungler, Nautilus do really need this item at start. Since Nautilus is a great AoE jungler he lack some damage on the big monsters in each camp, this will help him out alot. Also this item is used for Spirit of the Ancient Golem

5 of this in combination with Hunter's Machete is the perfect start for Nautilus, it gives him the damage he needs and the sustain.
This item is just perfect for Nautilus, it gives him Health Regeneration, Mana Regeneration and extra damage to monsters. And it's one part of the Spirit of the Ancient Golem.

Since Nautilus do have a low base Movement Speed, this item will really help him out, in both running between jungle camps and getting to lanes for a gank. A must have item on Nautilus.
You should finish this item pretty fast. It gives you a nice 500+ HP, 10% cooldown reduction, some health- and mana reagen, the bonus damage on monsters and Tenacity. Since you lack Tenacity from not having Mercury's Treads, this item will help you out. In general this might be one of the most important item on Nautilus.

A perfect item on Nautilus, gives your team a great sustain aura. And really nice stats for you. Before getting this item let your support know you will get it, since it's a very common item for supports.

Since all of Nautilus spells scales with AP this item is great, gives you bonus Ability Power, Magic Resist and a helpfull aura. In general a really great item, haven't seen a single game with a nautilus not buying this. Don't get me wrong but try to not get to many Ability Power items, you are not in the team to do damage,

Here is the item that might confuse people, like why not get Frozen Heart. I think Frosen Heart is a great item with Nautilus and very valid. But the Iceborn Gauntlet, have this extra AoE slow, more mana,30+ AP, Bonus damage after casting a spell, slightly less armor, and 10% less cooldown reduction and of course Frozen heart have a really great passive. But from my persnal experience Iceborn Gauntlet is a great profit for team, and fits Nautilus really good. Perhaps you think that it's not necessary to get it with Nautilus, sure if you already ahve it your team i would suggest Frozen Heart instead, but think twice before choosing.

This is the upgrade of Aegis of the Legion, it's a great upgrade if your team is struggeling with the enemies AP damage, I would always reccomend you to get this upgrade, maybe not at this point if thier team have only under fed AP damagers or such. But This item is a real profit for the whole team. And again tell your support that you will get this item.
As I said before it's a really great item for Nautilus, especially against AD heavy team. But once again think twice before choosing between Frozen Heart & Iceborn Gauntlet.

As Nautilus you really like when the enemy team stays together, so does Sunfire Aegis. The AoE damage really makes Nautilus a good damage output, even while not building for damage. But you shouldn't get this item if the enemies are AP heavy team, but if they are AD heavy team you should give this item a thought.

Might be my personal favorite item in the game, gives you bonus Movement Speed, slighty AP boost, nice amount of Magic Resist and a great activate ability: summons 2 ghosts that will hunt down enemy champions, slows them and gives your team vision over them. The activate is great for engaging a fight, escaping or to hunt down escaping peoples. Would recommend this item if the enemy team have a lot of AP damage.

Not a personal favorite for Nautilus, it sure gives you a great amount of health and health reagen. But as Nautilus this is often not necessery, I do prefer to get items with auras, activates and such. But if you have a huge problem with surviving this item might help you out.

I have seen many people recommending this item. I feel this item is more less focusing on dealing damage, which I don't think you should try to do with Nautilus, But if you do want to have damage output you might wanan consider this item. Personal I strongly recommend you to not get Rod of Ages.

This order for skills is the best if you want to play a bit aggresive, if you like to hunt down and finish people under thier towers you might wanna consider this. Why? maxing your W first gives you that extra shield, which will help you with diving towers. If you don't wanna dive towers and play less aggresive i recommend: This gives you a more slowing effect but not that huge shield. I recommend you to try both, and just see hows the game is going and decide after that.

In the jungle you need to move around a lot, with nautilus low base speed it could be hard to be at the right place always. So you will need to get T2 boots as soon as possible.

with Nautilus you should start at wolves and the go for blue. Then move to wraiths, after wraiths be prepared that enemy jungler can be at your red, people tend do counter jungle Nautlius. After getting to level 4 try to gank bot or mid, If not possible you should either back and buy or go for level 6.

After getting to level 6 you just need to move around as the game floats.

So in other words, move around between lanes, and be ready for counter junglers. Don't be afraid of using your ulti and other spells to disengage. NEVER build for damage. And CC the **** out of enemies.

If you feel that you want more/ or I missed information, just post in comment and I will try to answer your questions.

GL in the field.

Oh I forgot when there is time use /joke. Swimming in the air is awsome!