Awesome Nautilus guide! Nough said.

Frozen Mallet, Trinity Force (Only movement speed), Rylai's Crystal Scepter (only movement speed if spell is casted), and Randuin's Omen are some of the only items in the game with a passive that have a chance of slowing the enemy's attack and movement speed. SO make use of that on the fast melee attackers in team fights by focusing your auto attacks on them and trying to get them to attack you. (Also, be sure to utilize Randuin's Omen because that will automatically slow the surrounding units in both movement and attack speed)

Abyssal Sceptor reduces the Magic Resist of nearby enemies, so that will be useful for your allies who use ability power based attacks.

Shurelya's Reverie has a useful active skill that you would really only want to use when your team is running away or after an enemy or their team.

-His Passive is very useful on initial blows because they do extra damage, and they immobilize and enemy for a split second.

-Dredge line is more useful for pulling an enemy in or keeping them from running, so it is not really needed to max out by level 9. Use it in the bushes when you are laning, so an enemy will not see it coming, or when you know you will grab them successfully.
The cooldown is decent enough to use in the beginning of a team fight and even at the end for those who run away after your team killed their friends.

-Titan's Wrath is nice to have maxed out as early as you can because a massive shield makes you great for tower diving (though you shouldn't do unless you know it will work) and initiating fights early game. The skill, when active, does damage to enemies around the enemy you are attacking, so it make you pretty dang awesome. Nough said.

-Riptide is your baby maker, I would say. After using your Dredge Line on an enemy, it is good to instantly use this on them because it slows them and keeps them within the radius for your team to wipe them out. It is a great aoe and and reaches decently far, so use it as much as you can in team fights. Enemies who are slowed benefit your team greatly.

-Lastly, your Depth Charge. Be sure to use that right away when initiating a team fight. Always use it on the one who does the most damage so that they can stay immobilized. The last thing you would want is for them to wipe out you and your team and ending the game. After you use this, use your Dredge Line and Riptide and leave the damage doing to your team.
What's great about this, is when you use it on the big damage doer like Lux, Veigar, Xerath, etc., they usually stand far behind their allies, so it knocks up their allies as well.

Personally, I feel that Nautilus is much better laning than he is jungling.

When you lane with, always lane with a person who you know can do good damage like a carry, or bruiser of some sort. Nautilus is excellent at getting kills, but mostly at keeping an enemy immobilized or within a short enough radius for others to get the kill.

TRY NOT TO BE GREEDY. It would be better if you were to get your entire team fed off of kills, than it would be for you to get fed. You basically rely on other people doing damage while you immobilize your enemies. So get them some cash money $$$. Let your laning mate grab the minion kills while you hang out in the bush to Dredge Line your enemy. Your passive will also help for you to keep your enemy immobilized, along with Riptide. Worry about farming off of minions after your lane is cleared i.e. the enemy tower is destroyed and you have nothing else to worry about. Regardless, you will make cash money $$$ off of the assists and occasional enemy kills you will get.

When initiating a team fight, ALWAYS start it off with Depth Charge on an enemy that does the most damage. It is best for you to keep the person who is somewhat squishy and does a ton of damage immobilized while your team poops on everyone else.

Doran's Ring is needed in the beginning for the Mana Regen along with the small health and ability power. If you are going to want to harass and kill enemy champions a lot, then you will want to use spells which cost mana. Obviously, this will help alleviate that small problem.

Mercury Treads, of course, are always needed for a tank. No explanation required.
Building resistances will generally give your shield more effective health than building health. Abyssal Scepter helps both in tanking and increasing your damage especially since Nautilus is such a good initiator and often in the middle of the enemy team's zone in fights.
While Warmog's Armor does increase the damage amount absorbed by Titan's Wrath, it doesn't increase your overall damage output, making the enemy less likely to focus you during fights.
Frozen Mallet or Rylai's Crystal Scepter are better health items, as the slow can help you get more Staggering Blow hits. Glacial Shroud and its future item, Frozen Heart, are great item choices, allowing for better tanking with armor, mana to help with mana constraints, and CDR. Nautilus depends greatly on his abilities to deal damage so building CDR to counter his large cooldowns will allow you to do great amounts of damage to the enemy team.

Always buy potions when you have all of your items bought. You would be stupid not to.

Randuin's Omen is great for the small cooldown reduction, and the chance to slow an enemy's movement and attack speed. Especially if it is a strong melee attacker like Tryndamere with super attack speed. Also, it gives you armor, which is what a tank needs.

Trinity Force, is helpful for making you a very mobile tank. In addition, you usually always want to start out with Shen when buying Trinity Force for the Shen Passive.

Frozen Mallet is another nice item that enhances your health by a lot and has a nice passive that can slow an enemy's attack speed. That is always nifty when doing a team fight and focusing the super speedy melee guy.

Force of Nature is almost a given when it comes to tanking because of the nice Health Regeneration and the Magic Resist.

Shurelya's Reverie is needed for the great cooldown reduction that it gives, which is great for Depth Charge and Titan's Wrath, the Health and Mana Regen, and when you and your team are trying to run away from something scary (the active ability).

Teleport is useful for keeping towers from being destroyed and getting in on team fights quicker if there was an unexpected one.

Heal is just useful when your team does not have a support healer and it keeps you alive obviously.

Flash, is helpful for flashing into or out of a team fight. Also, it is always nice, since he can not use Dredge Line over or through terrain, to use it to get over or through terrain.

Let your teammates get the kills on minions (in the beginning in your lane) and especially champions. You will get farmed like crazy off of the assists you get.

After you have pushed you lane to the point where the enemy tower is down, you could either stay and kill minions for yourself, or you could get some buffs, OR you could gank the next lane.

Farming should be very simple for Nautilus as long as you stay active and tactical with him.

No greediness. I can not stress this enough. You are the tank and you will get plenty fed from occasional kills and assisting in other kills.

Try to keep your team alive by utilizing Nautilus' great crowd control abilities.

When it boils down to it, keep your team together, and try to avoid anybody getting ganked and killed before you can get there.

Do not let anybody die.

PROS

-Great at crowd control.
-Great at immobilizing his enemies.
-Great at getting his teammates kills.
-Great at farming.
-Great in team fights and initiating them.

CONS

-Easy at stealing kills if you are not careful to avoid doing so.
-Ranked might ban him, so try not to make him your main if you are going to play ranked.
-Dredge Line does not go over or through terrain (walls, trees, etc). It pulls you into the terrain instead. This can also be useful if you are running away from enemies.
-Dredge Line is slightly difficult to use properly when ganking in the jungle.
-Personally, I think that Nautilus is not that great in jungling as he is laning.