Start hunter's machete and four health potions and then head over to red buff. Yes, red buff. Get your leash and activate your shield as soon as you start fighting it. You'll make it out with plenty of mana, trust me. Then take wraiths using your shield and AOE only once each. Then go to blue buff, you'll have enough mana to use your shield and AOE once each on that as well. Now you have both buffs, almost full health and mana if you used your shield properly, and your three base moves, so start ganking!

When you gank, obviously pull someone in with your q first, unless you can get close enough without having to use it first, That way you can save it for when they try to get away. Immediately basic attack them to get the root off and then use your AOE slow. Walk in fron of them so that it's harder to get away. You're a giant, fat, titan of the depths! Throw that weight around and don't let them walk around you! You'll be very successful with this strategy.

Between ganking, you'll be farming the jungle. I path from one side straight to the other (ie golems-wraiths-wolves-white-repeat or vice versa). If you go in this circle you'll make the fastest clear time. Don't stop at one camp on your way back to the first one, because then it isn't up when you go back to it and you're taking longer. You want to clear as many camps as you can as quickly as you can.

In teamfights, and I kid you not, you're an assassin. Make your way to the back with your buddies and kick in the carry's teeth. Try and ult the person in the back of the team so that it goes through and knocks up everyone on its way. Nautilus is such a tanky bully that you can easily charge through everyone and slap a carry. On your way, try to get your passive off on everyone and keep everyone off of your carries. Nautilus is very good at making people go where he wants them to, so use that.