Yes, it may sound weird, but NASUS AP became stronger after the release of runeglaive earlier this month. By purchasing runeglaive, you deal magic damage on your Q, but you lose the ability to heal using your passive, that's why I highly suggest you build will of the ancients(see? problem fixed). Also, when you completely finish your build, you will be surprised to see that your E deals 500 damage constantly on almost every target, while your Q is pretty strong to go in a 1v1 safely.

By minute 40, you should reach 400-500 stacks while farming the jungle using those hybrid penetration runes will turn you into a beast, a solo queue destroyer!

Before saying it's a bad choice, you should try it for yourself. And as good news tend to come one after the other, runeglaive will be buffed and Nasus will also grow in strength and become a safe tier 1 pick.

You should look to start gromp on each side as you need the blue buff pre level 3 to clear the jungle faster.
The correct jungle path is: smite gromp - blue buff - top/bot side rift scuttler(by killing rift scuttler early game you get the chance to regen a huge percentage of your total health and also put pressure on a lane as you don't allow the enemy jungler to gank early) - smite red buff. After you finish this path, you should be 3 and half. That's understandable(it's how the jungle is built), so you should look to do one more camp - preferably wraiths as they are easier and provide a lot of experience and gold income. Then you should aim to gank bottom lane(if your support is Thresh/Blitzcrank/Morgana) or top lane(if your enemy top laner is weak early game by going through the lane bush(Unnoticed of course). Doing this will also allow you to "steal" experience from the lane minions and get level 4 to add a point to your W. After you are 4, you can easily gank almost anyone and AT LEAST get rid of one of his summoner's spells.

You should run ghost smite on Nasus as flash is pointless. Chilling smite + ghost + W will make your enemies tilt as they won't be able to escape from THE DESTROYER!

Also, something that's a MUST-DO is to keep your Q at all times and use it to kill the monster(this way you'll gain stacks faster).

TL;DR Easy to play champion, free elo, outscaling potential.

This chapter is very important and must be understood completely. Team work is the main factor that brings you the "Victory" screen. Nasus isn't really the champion to build team synergy, but it can work with his team just fine.

The way you want to play around your team is this: you let your front liner(top laner I assume) to tank the incoming poke(like Corki's ultimate) and you look to throw your E on squishy targets. If the enemy team outscales yours, you ask your team to kite and bait them while you go and split push. If they want to counter you, they must send the powerful players to stop you and you can easily outdamage and 1v1 them.

Those are the best tactics to win with Nasus AP.

PROS:
1. You deal a lot of damage and become unstoppable after a point of the game.
2. You can sustain the jungle easier than most of the actual junglers.
3. You can look for objectives almost as fast as Nunu.

CONS:
1. Your ganking potential is reduced as you can't do anything else besides using your W.
2. You can get invaded and can't response to it.
3. You are weak against early game junglers, especially those that are a bit cheesy(Nunu and Evelynn)

Nasus is a strong pick in almost every team comp, besides those that look to win the early game with pressure from their jungler and a strong laner like Corki.

You should make sure your top laner is tanky with early game pressure, like Irelia or Maokai. Gnar can work too, but those are stronger. Your mid laner should be a long-range poke based champion like Varus or Jayce, but Ezreal is working perfectly fine too.

You should avoid picking Nasus against poke comps unless your team goes for full engage(Righteous Glory on Thresh support, Maokai top, Kalista adc, Azir mid lane is an example).

Other than that, enjoy free elo!