There are 2 schools of thought with Nasus.
1. Go DPS with Siphoning Strike. It's kinda meh IMO, but maybe I'm just not as good at it.
Level up Spirit Fire to max for the farming
Level up Siphoning Strike as a second priority for increased usage
Level up Wither once to begin with for your ganking purposes.
Skills are Exhaust/Rally/Teleport(eh... not my fav)/Ghost
Masteries are usually maxed 21/0/9.
The offense tree goes 1/1 Cripple (if you grabbed exhaust) 3/3 Deadliness 4/4 Alacrity 3/3 Sunder 1/2 Offensive Mastery 3/3 Brute Force 1/1 Improved Rally (if you grabbed rally), 1/1 Havoc.
Utility is 3/3 Perseverence 1/3 Good Hands (Swap for something else if you got ghost/teleport) 4/4 Awareness.
Runes I stack MS for chasing, CD reduction on Blue, Armor Penetration on Red, and whatever's left over on Yellow. Health, Dodge, are all fine.
Sapphire Crystal + 2 health pots
Boots of Speed
Treads of whatever, look at their team to decide
Stark's Fervor- the reasoning behind this item, and not something else is...
1. You're going to be in the middle of things. Your ult encourages it by draining hp away from them, so to maximize it you need to be surrounded by enemies. And unless your team has just totally screwed you over, your allies should be with you too.
2. The armor debuff works well with Spirit Fire. Other carries will love you for it, because it makes them stronger and their enemies weaker.
3. How else are you going to stack lifesteal? Executioner's Calling increases your chance to crit... and unless you've gotten crit damage runes already, it doesn't help as much. Somebody else did the math on this one, not me, I'll try and find the post. Bloodthirster's requires kills to work, and also for you to not die. Kills you can work with. But deaths... The survivability with DPS Nasus is honestly not that great, one CC and you're pretty much screwed if you aren't lifestealing.
One survivability item of your choice: you need the survivability in order to get the full duration out of your ult. Guardian Angel is a decent all purpose item, but if they're stacking AP/Phys specifically there are better options.
BF Sword - increased damage, yay! Pretty much a given for any dps character.
Trinity Force - I feel that getting this before the BF Sword makes you more reliant on your initial triple cast combo, and not DPS-y enough. Dunno, experiment with this one yourself.
Bloodthirster/Infi Edge/More BF Swords, whatever you want. The game should really be over at this point.
2. The Tank build.
There's a million other guides/words of advice on it. Aegis, Warmogs, Sunfire Cape, Sheen, etc. etc. Not covering it.
3. Farmer/Anti-Phys build (aka, I lied about 2)
I really wish I'd thought of this, but I didn't, Lee HWAITING did. So yeah, full credit to him.
The way this works is with phys carries dominating the current metagame (twitch!yi!trynda!), and casters almost nonexistant, you lose most of your ap resist for armor, and the ability to farm well enough to go toe-to-toe with carries late game.
Go 1/21/8 or 1/8/21 with this build. The one point in offense is for exhaust, which is great against almost all phys carries.
Runes: Standard Nasus runes, 3x Quints of MS, etc. etc. Whatever floats your boat really. I've been using caster runes for a better early game.
Ult is your priority
1 point in Siphoning Strike to last hit with in the beginning
Max Spirit Fire for farming
Max Wither to help shut down phys carries
Max Siphoning Strike last
Start with the Sapphire Crystal + 2 hp pots, then build into Sheen.
Go Mercury Treads for the only ap resist you'll have, I don't recommend going for any other shoes unless they have literally no CC whatsoever, because this is again, your only ap resist whatsoever, so it's pretty **** important.
Stack 4x Heart of Gold.
Yes, that's right, stack four Hearts of Gold.
As retarted as it sounds, it really does work... as long as your enemies are pretty much all phys dps. The armor to hp ratio is pretty **** good, and with an extra 2 gold every second, you could be dead for half the game and still farm like a god.
Which isn't going to happen, right?
Then buy your Trinity Force all in one go.
2870 is the magic number I believe, and it's really not that hard to hit with 4 fricking gold generators and an amazing farming skill.
Buy whatever you need. Thornmail, Sunfire Capes, whatever floats your boat at this point.
Siphoning Strike should be doing large portions of their hp at this point, and you should be reaching what, 70% damage reduction? Laugh that in Twitch's face.
Editing this later because it was a sleep-deprived rant.