First, the general tips:
-
Try to avoid shoving Nasus under his turret. That makes him very hard to poke and/or kill as most melee champions, leaves you overextended (and wither makes it very easy for his jungler to gank), and limits your jungler's options.
-
Nasus will typically stack resistances. Nasus built a lot of armor against you, so switching lanes with your Kassadin would have been a good idea. Kassadin is really good at poking out melee champions due to his mana sustain, the burst damage on W, and the poke on Q. Hecarim would have worked very well mid-lane, since you could easily roam bottom lane to help them snowball.
-
Nasus deals primarily physical damage and he doesn't usually itemize for armor penetration. If you believe you will have to split-push against him for a significant portion of the game, you want to purchase some armor. 
and 
are especially useful when dueling him since they will reduce and reflect damage from his Q respectively.
Shoving to tower is the absolute last thing you want to do against Nasus. It lets him safely free-farm and sustain, limits your trading opportunities, prevents your jungler from ganking him (in most cases), and leaves you vulnerable to ganks (and Wither is great for chasing people down a lane). Diving Nasus can be risky as well since:
- Wither slows you and lets him escape
- Spirit Fire reduces your armor, amplifying the damage dealt by the tower
- He can get a large burst of health from his lifesteal and his ultimate
Now for your questions.
How do I deny farm?
In my experience, I find that you have to freeze the minion wave and zone Nasus from farm. If at all possible, try and get the minion wave pushing towards your tower, freeze it, and call your jungler up to gank Nasus while he is overextended.
A good Nasus player may know how to handle this situation and break the freeze, but if you can get an advantage against him you can often bully him early. Just make sure he spends as little time under his tower as possible, since they is where he can freely farm and sustain.
Do I roam or stay top?
This greatly depends on the situation. Many counterpicks against Nasus will want to stay in lane with him and deny/bully him for every CS he tries to get. This works quite well when you can do so for an extended period of time, but this isn't always possible (especially when your team is losing). If your champion isn't good for handling Nasus or your team is having issues, you may have to roam to try and snowball other lanes. This can help you end the game early, snowball your team to victory, or get you allies fed enough to help against Nasus. This can be really risky though, since it allows Nasus to freefarm and splitpush.
What champions do I pick into Nasus?
Generally, I find you want some mixture of the following quantities in a champion laning against Nasus:
- Durability (to survive retaliation and ganks)
- Sustain (to stay health and outsustain him)
- Spammable abilities (to punish Nasus whenever he tries to CS)
- They have some method of sticking to Nasus or don't rely on attack speed (since Wither can cripple many opponents)
- Anti-tank abilities (armor reduction, percent health, etc)
In addition, it helps if your champion has a strong mid or late game so that they don't fall off in comparison to Nasus. From playing as and against them, I find that the following champions can (or could) do relatively well in lane:
However, you don't always have to counter Nasus solely in lane. There are many champions in other roles who work very well against him.
**Mid laners: **
These champions typically offer high sustained damage and methods of kiting Nasus when he tries to approach their team.
ADCs: 
These ADCs primarily have CC (knockbacks, slows, snares) for kiting Nasus and deal either mixed damage or highly amplified physical damage. Several of them have percent health damage or anti-tank abilities to help kill tanks like Nasus quickly.
Due to the crippling effects of Wither, your ADC should typically have either 
or 
. This can let them remove Wither immediately and kill Nasus before he can reapply it.
Junglers: 
Junglers can be tricky since you typically want someone who is strong and capable of kiting him late game, but you also want someone with strong early pressure to gank Nasus and set him behind.
Nunu can set the enemy jungler behind, relieving pressure from the top lane so they can keep bullying Nasus. During teamfights, he can buff your ADC to increase their damage, chain-slow Nasus to prevent him from reaching anybody, and is too tanky for Nasus to kill.
Master Yi is a special case since he isn't that great against Nasus in teamfights but he can absolutely murder him when they splitpush against one another. Master Yi can deal a lot of mixed damage (Devourer, Blade of the Ruined King, Wuju Style), build somewhat tanky against Nasus (Ninja Tabi, Thornmail), can use Meditate to reduce Q damage, and ignores Wither. He deals far too much damage for Nasus to heal through and deals it too quickly for Nasus to kill him.
Supports: Pretty much the entire support pool can help counter Nasus due to the CC they provide and how good they are at kiting/peeling immobile squishy champions from their carries.
What summoners do I take?
You typically want to take Flash and Teleport. While Ignite gives you some extra kill pressure, you may still lose your level advantage if you have to walk back to lane. In addition, if you don't have teleport than Nasus can freely splitpush and still join fights so you will either lose towers 1v0 or lose teamfights 4v5.
What do I build?
That greatly depends on the champion you are playing. However, I would recommend building your percent-penetration items relatively early in the lane since Nasus will be stacking resistances against you. Afterwards, you may want to get some armor (such as Ninja Tabi, Chain Vest, Seeker's Armguard, or Warden's Mail) or continue building damage.
If you want an example, I would typically build Ionian Boots, Hextech Revolver, and Void Staff as Vladimir when laning against Nasus (or most tanks) so that I could quickly poke him out of lane and prevent him from sustaining through my damage. As Darius, I would recommend rushing Black Cleaver into Randuin's Omen to render his armor ineffective and to become durable enough to ignore his damage long enough to kill him.
I hope this helps. If you have any questions, reply to me and I'll try and help if I can.
which is core on him.
+ 
or