Sample Full Build
Nautilus has very few bad match-ups in top lane right now, and almost always out-scales his competition into team fights. He's also very strong for dealing with squishy champions in the top lane, and has some of the best gank setup, probably second only to Maokai.
Solo lane Nautilus is a hyper-tank. He provides incredible CC in late game fights, and is very difficult to kill. As such, in most games, your focus should be on making him as difficult to kill as possible, and capping out his CDR.
Frozen Heart: Once you have a bit of a health pool up, this is your best option for ramping up your tank stats and CDR quickly.
Iceborn Gauntlet: A damage-heavy option to Frozen Heart. It's an excellent choice if you're winning lane after your laning core items are complete, and want to push that advantage. It's also an excellent choice if you're less concerned about the attack speed of the enemy team.
Spirit Visage: This is the best Magic Resist item on Nautilus, and depending on your rune choices, might might cap out your CDR in conjunction with Frozen Heart or Iceborn Gauntlet.
Sunfire Cape: While not exactly a core item, you'll often complete this item to help you control and win lane. Not usually ideal to build after laning phase.
Ninja Tabi: These are your go-to boots.
Mercury's Treads: Build these, only if you're worried about CC completely shutting you down.
Liandry's Torment: If you do snowball your lane, you can sometimes afford to pick up this item. For a tank, Liandry's Torment on it's own will provide you with absolutely ridiculous damage output, particularly against the squishier targets on the enemy team. If you're not winning, and/or your team isn't going to be lacking damage, there's no room to build this.
Randuin's Omen: If you're doing your job correctly, you will be getting hit a lot in fights. This is your best mitigation to remedy this problem.
Guardian Angel: An excellent 6th item. Allows you to really go all-out in fights, without worry.
Thornmail: If you have a lot of health, and are the focus of auto attacks, build this.
Zz'Rot Portal: An alternative to Guardian Angel. Sometimes can be built sooner as well. A good option if your team is on the back foot.
Dead Man's Plate: Build this instead of Sunfire Cape if laning phase is over by that point. Usually Randuin's Omen takes precedence.
Locket of the Iron Solari: If Spirit Visage isn't enough magic resist, and the enemy has a lot of AoE, build this.
Build one of these to cap out your 40% CDR if you're missing due to runes (or a full AD enemy team).
Warmog's Armor: Excellent item on Nautilus, given his massive health pool. Works very well with Thornmail.
Banner of Command: Budget armor, CDR, and Utility. Not a bad buy, but not usually optimal. If you ever forego Frozen Heart and Iceborn Gauntlet for some reason, you could consider picking up Banner of Command to help fill out your mana pool and CDR instead.