Nasus is a solo top fighter. He is extremely balanced and if played right (a.k.a. this build!) you will become a force to be reckoned with. This build is for both New players, and ones looking to destroy with Nasus at all ELO levels. You will make your foes bow before the might of:
I build Nasus a an HP heavy, hard-hitting, CDR maxing anti-carry. This makes it sound like he can do a lot of things at once, that's because he can. He has lots of utility in both his Wither and Spirit Fire plus tons of damage in a correctly farmed Siphoning Strike, thus he doesnt need to build items for damage he can just further his utilty (through Randuin's or Shurelya's) and tankiness (Warmog's, Force of nature) while grabbing damage long the way(Atma's and Trinity force).

Pros:

You are a tank but still deal tons of damage.
You are an anti-carry.
Gank resistant. (due to W over time slow)
Can super push lanes and Obliterate turrets. (remember you can use your Q on turrets)

Cons:

You are super farm dependent.
Its easy to get overconfident (e.g. Taking on a 1v5).
Very expensive build. (Philo-stone helps)
No hard CC and thus not the best tank for engaging.

Laning Phase:
Farming! Your Q ( Siphoning Strike)is your main damage throughout the game. If you make sure to constantly last hit with it You'll be tearing apart your enemies (especially those squishy carries) late game. For this reason only play nasus in a solo lane; he NEEDS to farm undisturbed (thats why you have wards so you can pretty much avoid damage from ganks) for most of the laning phase. In case you don't know Nasus' Q gains damage with every thing that you last hit with it; therefore, it is necessary to last hit with it essentially on cooldown and not to harass with it against your enemies in lane.

When the jungler, who you have spotted with your down river ward (see Panglot's warding helper: Your text to link here...) jumps in to gank you just simply W ( Wither) him, and run. if they decide to turret dive you play hit and run under the turret as your Q gives insane amounts of lifesteal, plus once you've hit six you can bait with your ulti for a kill. This said if you know the jungler is coming to gank you and the enemy minions are pushing, don't run away immediately, make him waste his time, BUT DON'T Push your lane cause you're over confident. Essentially with Nasus just don't engage nor get engaged upon.

Another note: don't use E ( Spirit Fire) to farm as this will gobble up all of your mana. It's only used to lower armor on targets and to push minion waves late game. The only exception to this is if you are being heavily denied and even then just ask for a gank from you jungler as getting your Q farmed is a priority for you whole team.

Mid Game:
By now Skirmishes are breaking out everywhere and you have have to be there for your team. Your Warmogs should be done and you are the main tank so always lead the charge. (your role in teamfights will be discussed further in the late game section). Make sure to spam Q on everything and even while just walking by minions always Q off of cooldown to maximize your Damage later in the game. This is where a lot of people fail as nasus: they know how to Q farm in the laning phase but after that they just cant keep up. Your Q damage should always be increasing.

Late Game:
Now you are an Anti-Carry. All of the damage dealers on the other team are scared of you and thus your carries are safe. You are essentially an unstoppable bully. You are there to either scare them away from your team or scare them unknowingly into your team waiting for an ambush. In team Fights You should initiate with you ulti and Shurelya's Battlesong and Wither the AD carry. now throw down you Spirit Fire on wherever your ad carry is targetting to help him out with the armor reduction. Then continue to bash people with you Q (preferably their AD or AP carry). If you get engaged on in a undesirable position or if their bruiser is dealing heavy damage to your carries, whither this pesky bruiser and let him be kited and killed.

greater mark of desolation and greater quintessence of desolation:
You need armor penetration as Nasus. Your Q is useless without this penetration. Period sorry that's just a fact. SO we take both armor pen quints and marks.

greater seal of replenishment:
Greater seals of replenishment are need as Nasus tends to be very mana hungry throughout the game. The combination of these seals and the Philo-stone makes for a perfect amount of mana (not overkill). Just don't spam your W and E.

Greater Glyph of Cooldown Reduction:
Just like Armor pen, Cooldown reduction boosts Nasus so much. In teamfights Spamming that mega Q and controlling those carries with you W (remember anti-carry) will win you fights. Being able to spam all that utilty(your W and E) and pure damage (your amazingly farmed Q) is key plus by the end of the game due to you Shurelyas, these glyphs, and masteries you will have just barely capped CDR. Best thing ever! these glyphs are also key early game in being able to last hit more often with you Q.

Since we are going for High amounts of HP, Juggernaut and the defense tree is key. Grabbing CDR in both offence and defence maximizes you DPS and utility. Also we take Indomitable over Evasion because the carries will be targeting you and they have single target damage.

philosopher's stone
This item helps with Nasus' mana problems and helps with all that money he needs for his build. Starting with the Faerie Charm gives that needed mana regen and going back at 1000 gold gets you the Philo-stone and boots.

Warmog's Armor
You build this item first because you don't need damage until mid-game. As stated earlier You are just farming and staying alive through all those annoying ganks in the early game. Another reason for getting this item before trinity force is to let it obtain full stacks ASAP.

Sheen and Trinity Force
Of course you can get Sheen after you get your giant's belt and before warmog's, but it will slow down your overall build. There are situations were you should get sheen this early, especially if you are against a very squisky top lane with no harass, or if you get an early turret meaning you can roam more. Setting that aside, Trinity Force is an amazing Item on Nasus due to the Sheen proc, movement speed bonus and overall stat bonuses.

Atma's Impaler
Now that you have lots of HP it's time to get Atma's. now you might be saying to yourself "OMG NOOB another ATMOGS BUILD BLAH BLAH BLAH QQ" but atma's is a bout building health and nasus is about building health (at least in this build)... so its the perfect item, Deal with it :)

NOW COME SOME TOUGH DECISIONS:

Whether to build Force of Nature, Shurelya's Battlesong, Randuin's Omen, Aegis of the Legion, or Bloodthirster
the first three are more anti-carry oriented, the last is just a great team oriented item.
The best combinations are:

Force of Nature then Shurelya's Battlesong:
All around good combination it creates good initiation and lets you rush right to the carries with super moves speed. Plus very good chase.

Force of Nature then Randuin's Omen
Are the ranged carries super fed? stacking phantom dancers? then look no further, less initiation but you will still move fast enough to get close and use that randuin's. Won't really have the CDR from shurelya's but all builds have their pros and cons.

Aegis of the Legion then Shurelya's Battlesong
The team oriented combo: use if they have good anti-carries or keep getting great initiation on you.

Bloodthirster then Randuin's Omen, or Force of Nature then Bloodthirster.
These are good choices if you already have a tank with good engage (a.k.a. Amumu, Galio, etc.). This tank will probably have shurelyia's reverie and so will your support so don't take that. Since you are an anti-carry Randuin's Omen is always a good choice, but since you MR is low The second choice is often the better unless 80% or more of your opponents main damage is Physical.

Infinity Edge and Phantom Dancer
TROLL but works surprisingly well... don't use this in serious games... but if you get super fed, why not?

My notes on other items:
Guardian Angel:
I used to use this in my build but I feel it doesn't make a difference. By the time you get it it might only pop once... and yes the resistances are nice but there are definitely better items on Nasus.

Banshee's Veil:
Just doesn't seem to fit anywhere in this build. You already have enough MR from force of nature.

There are other ways to build Nasus of course (as there is with every champion) and still be the beast that he is but I just find this to be my favorite and most effective way.

Flash and Teleport work best for Nasus. He needs teleport to be everywhere and catch up with his team if a fight breaks out late game and needs it to get back to farming early game after blue-pilling. Remember, late game you can use Teleport defensively, it can be used on an allied tower far away if you get caught out of position... since you will have tons of HP you will get away in time :) and your opponents will be like "wtf?!"

I can see Ignite working to finish off foes in lane especially sustainy ones (e.g. Vladimir) And getting a fleeing foes while W is on cooldown. Ignite is better on other champs preferably.

Also, Exhaust might be a good choice since you will become an anti-carry and thus will be close enough to mitigate all that damage and prevent that squishy AD from getting away. Just remember it is exactly like a second Wither and thus should not be stacked as you will get diminishing returns and a reduced time on your overall combined slow time.

Heal is good on champs with lots of resistances as the health it replenishes is worth more as taking it away is harder, but since we are building HP, the percentage of total HP that it heals in not even close to worth it.

Please be aware due to the inaccuracy of the cheat sheet (it doesn't factor masteries nor items' passives) Nasus' health with full build and ulti is closer to 5000, his attack damage is closer to 250 (PLUS super damage Q and sheen proc every 2-3 attacks) and his CDR as stated earlier is maxed (if you take shurelya's).
In case you haven't realized, This is a Lane Nasus build. I'm aware that he can be jungled quite adequately but his Q-farm is significantly hampered.

Thanks for reading and please rate and/or give me suggestions

I'm happy to correct myself or clarify :D