This is how i have been playing Naut, and trust me when i say the damage he puts out is very underestimated. People expect him to be a tank and do mediocre damage. Also keep in mind I play with this build extremely aggressively, and it pays off. With this build, he is still tanky, but can do over 1k dmg in a single burst at lvl 11. then live through any return fire and chase any survivors. His CC is crazy and mixed with a carry, not much can stop him. He is the perfect initiator and unless focused entirely, can shut down and kill the enemy carries.
This is still a work in progress but this is the best build ive played on him so far.
The best place for this build is bot with a carry, not so much a solo build.
I use my basic caster rune page, armor, magic pen, and ap. It makes him a serious threat early game, and can steamroll you into the mid game, at which point you are fed enough to faceroll the rest of the game. Pretty self explanatory.
Start with the ring, the hp, regen, and AP is all you need for early game and keeps you in the lane a long time.
I then rush Catalyst, giving you sustain to last through the laning phase and sets you up for a Rod of Ages.
But before you finish the Rod, get Sheen, mixed with his passive, it makes his burst crazy early game. Dredge Line to close the gap, smack em with the Sheen proc and you wil have done at least 400 dmg at lvl 6 or so.
After the Rod of Ages, i then go for Zhonya's Hourglass, giving him more tankyness and a large chunk of AP.
Then at this point, if they havnt surrendered yet, I either go for Lich Bane or Rabadon's Deathcap, just depending on wheter i need to smack em more, to blast them more. Then obviously get the other, and by this point, nothing can stop you aside from extreme cc but even then, you are tanky enough that it will take a long time to to kill you and the rest of your team should be able to mop them up.
This is my first guide, hence the short and sweet presentation. Please tell me what you think and if this build worked for you, and any suggestions. thanks for reading.