Hello, and welcome to my GLORIOUS guide to Jungling as Nautilus. Nautilus is a very beefy tank that can absolutely rip champions apart in both the early and late game with a combination of AoE spells, grabs, and just downright slamming people to the ground with basic attacks.

Early game is fairly simple really. Eat the jungle and ganking lanes. In all seriousness though, jungling as Nautilus is very straight forward. Starting at blue (You should hopefully not anger your mid and top laners before the games starts for this to work) you might as well Smite that, move on to the wolves, wraiths, Smite Red Buff, and then move to the golems. Down pots whenever you can... Mmm, red stuff. After than, you can maybe afford to start ganking without even getting boots, it's really up to you whether you would prefer a stronger, later gank or an earlier one.
Alright, on to ganking!

When you gank as Nautilus, the most important thing to remember is to save your grab in case they try to escape your grasp. Emphasis on try, by the way. ;). If you simply walk into a lane with Titan's Wrath up and hit the poor fellow on the receiving end of your damage with Staggering Blow, then they will most likely start to panic and burn off some form of movement ability, such as Flash or Ghost! After they have burnt through this initial feeling of safety, slam into them with a Dredge Line and show them why they are on the wrong side. Follow this up with a Riptide, and then after a few autoattacks and of course the help of your adoring fans (The person you are helping in lane), they will either die (this is preferable), use another movement ability, or run like a coward and die to DoT. They can escape, but if they did... You did it wrong. Keep on jungling and ganking for the next ten/twenty minutes, and don't forget to give your mid a blue buff every now and then. That way the mid laner won't shout at you.

In teamfights, you should be soaking up as much damage as inhumanly possible, as well as showing those squishy carries and mid laners who's boss. The amount of disruption and AoE damage a Nautilus can throw out can often be a shock to the enemy team, so keep this in mind when you are in the middle of a fight. But your main focus should still be on being more or less a "wall of meat" for your squishy compadres (tank damage, piss off enemy squishies). However, if you see a kill opportunity, go for it!