Nasus Beast Mode : ON

Ok, this is how this goes.
Every now and then, you get a jungler, and somebody has to take the solo lane, Nasus is great at soloing, and you shuold ask for it, cause it means you get your Ult faster (R skill), and more gold, wich makes you stronger.

Summoner spells:

I take ghost and teleport.
Ghost is great for allmost every champ, you need to save another a teammate, you need to save another lane's tower (when teleport is on Cooldown of course) and obviously if you need to run away or chase somebody.
Teleport, well if you have fast pushers on your solo lane you are going to need teleport to get back to your lane after shoping your items.
Why not flash?
Well i was a pretty big fan of flash before they nerfed the posibility of dodging a projectile with it, you can't longer dodge tower hits or stuns or ranged attacks with it, wich usually gave you the chance to overextend a little bit more while coming out alive. That's why i dont recommend flash unless you are Too squishy and you need both ghost and flash.
Cleanse
You might wanna get this, Because an exhaust can completly neutralize you, and then get you killed easily, since this build is based on damage and the 40% lifesteal from items and Passive you wanna be hitting something All the time in teamfights.

Runes:

I take Crit chance Marks, Mana regen per lvl seals, Flat Cooldown Reduction Glyphs, and Flat Healthpoints Quints.
Don't underestimate the Mana regen per lvl runes, cause they keep you full at all times.
If you dont have any mana you can only autoattack in teamfights, and that is not Nasus best.

Masteries:

I take 21 in offense and 9 in utility.
In offense i take, Critical chance and damage, magic penetration (for our Spirit Fire and our Ult, Fury of the Sands), Armor Penetration, and Attack Speed.
While in utility i take improved Ghost and Teleport, Experience bonus and Greed.

With Spirit fire, and Greed you will stack gold like crazy to get your items eariler, and to be in advantage.

Items:

The core build isBerseker Greaves,Manamune,Trinity Force, andStarks Fervor.

After this if you are doing good and your survivability seems good, you can carry on with the full build for more damage and a Lot of critical chance,Phantom Dancer to maximize Crit chance and attack speed, and of courseInfinity Edge for the Base damage and crit chance boost and the passive wich is huge at this point with allmost 85% critical chance.

IF your survivability is low cause they are focusing on you Too much, getting nuked, etc. i recommend gettingWarmogs Armor wich gives 970 Health and 30 health regen per 5 secs. I know the usual pick for a DPS would be Frozen Mallet, but you allready have the slow in the Triforce, so it would be a waste of a passive, plus the warmogs gives allmost 300 more health and 450 more with the passive maxed (Permanently gain 4.5 Health per minion kill), wich is incredibily easy with nasus cause mid-late game you can just lay down a spirit fire, run back and you get allmost the full minion wave.

Well since we wasted 1 slot on survivability we are going to loose some offensive item. After getting warmogs, get Phantom Dancer, Then get the money for Infinity Edge, sell Manamune and buy Infinity Edge, And try to get Blue buff whenever you can to be full on mana. Still, runes at Lvl 18 are doing a pretty good job at it.

Early Game:

If you are soloing, you wanna take top lane, so the jungler has 2 champions in the lane near to Dragon, wich is very important for him to be safe while getting it.
GetMeki Pendant, And2 health pots.
If they are harrasing you a lot, just stay by tower, pop spirit fire to farm the minions, try to get as much last hits as you can, if they are not hurting you much, stay in range of exp, use spirit fire on the minions, and get last hits.
This is very important, you must last hit as much as you can withSiphoning Strike, cause you gain permanently 2 extra damage on that Skill every time you last hit any enemy unit.
Do not underestimate the power of it, if you learn to last hit very good, you will get a huge bonus later on.
Stay in lane as much as you can, try at least to get the money forTear of Godess, its only 600 gold to it, since you started with Meki.
Go back to lane, keep farming and last-hitting, getBerseker Greaves, andSheen.

Mid Game:
By now you shuold be finishing yourManamune, and Getting eitherZeal orPhage, to later finish theTrinity Force.
Start building upStark's Fervor with theLifesteal first, then get theAttack speed.
Once you built Triforce and Starks, you are doing some really Serious damage.


Late Game:
As i said earlier, either getWarmogs if you are getting punished a lot, or go straight forPhantom Dancer andInfinity Edge. By this moment pretty much everyone goes down to you.

TIPS:
THIS IS VERY IMPORTANT
A lot of people tend to think they are "tanky" cause you know... its Nasus, he is tough, he can take punishment. WRONG
You are a DPS you are not suposed to initiate, let the tank initiate and then go in. Lots of people think that just because your ult is up you can go and start a fight vs 5 champs. Don't make this mistake, yes you are a bit more tanky than other DPS's out there but you are still weak enough to die against multiple targets.
Also, never stop growing Siphoning Strike, even late game, cause it has no max limit. The longer the game goes, the stronger your Siphoning Strike can be.
One good way of hitting hard faster is pressing Q or activating Siphoning Strike, right after you landed a basic attack. It will land your Siphoning a Lot faster, this is a great techinque for pushing towers and inhibs.
And never forget to use your spirit fire on the battle, their armor gets lower and you hit harder.

This is about it with the Build. I will update a little more.
And of course i would love comments on downvotes and upvotes, just to improve the build and hopefully get better.