Wither is best used to shut down auto-attack dependent champions, slowing them to a crawl and reducing their attack speed dramatically.
Choose your target wisely (usually a carry) when casting, as the moderate cooldown isn't very forgiving if you choose poorly.
With high amounts of cooldown reduction, Nasus can almost continuously maintain Wither on the enemy team (5 sec duration, 6.6 sec cooldown). However, enemy tenacity can counter-act this.
Without any gap-closers or mobility, Nasus relies on his Wither to protect himself from being kited.
Be careful when using Spirit Fire near your tower, as it will push the lane and you will lose last-hits.
During the laning phase, Spirit Fire will discourage your enemies from farming, but it has a relatively high mana cost.
Nasus's ultimate can be used at the start of team fights as you will be doing constant AoE damage to enemies while gaining attack damage for big hits. It can also be saved for the end of a fight to bait enemies with the health boost (stronger in small fights).
Fury of the Sands can be used offensively or defensively, use it to catch or escape enemies, as it also gives a massive health boost.
An alternative is to build Athene's Unholy Grail. This serves several purposes; it gives Nasus a little magic resist, which helps him tank, grants an essentially endless mana pool, and gives cooldown reduction, which allows him to more easily farm Siphoning Strike, and use his other abilites more often.
Whilst generally considered inferior on Summoner's Rift, this type of build is more favorable on other maps due to lack of opportunities there to farm Siphoning Strike; this is particularly true of the Howling Abyss.
Do not make the mistake of purchasing Tiamat or Ravenous Hydra on Nasus as the items have almost no synergy on him whatsoever. Not only do enemies killed by the Cleave passive effect not count towards increasing the damage of Siphoning Strike, but neither the Cleave passive nor the Crescent active even apply any of the bonus damage of Siphoning Strike, since the damage they do is based solely on Attack Damage and does not include on-hit effects. More importantly, the splash damage will cause minions to die faster, making it considerably harder for Nasus to farm Siphoning Strike effectively.
However, the passive and active do greatly help with Nasus' split-pushing abilities (something he excels at due to Siphoning Strike's ability to let him take down turrets rapidly), and also proc the life-steal both from the item itself and from Soul Eater, adding to his survivability in team-fights. All this makes it a relatively effective late-game choice on Nasus in a more offensive build.
Randuin's Omen is an excellent armor item on Nasus, as it makes him more difficult to kite, which, despite Wither, is still one of his few weaknesses late game. The active also becomes more effective the more resistances you build, making it especially effective on a tanky build.
When itemizing for defenses on Nasus, prioritize resistances over straight health, as this will make both your innate life-steal and the bonus health from Fury of the Sands more effective. With that said, do not neglect to purchase health entirely, as when you have built some resistances, these will cause it to scale rather well.
Consider using life steal Quintessences on Nasus; they are the most effective sustain tool for him. This is because his Siphoning Strike procs life steal. While the damage of Siphoning Strike rises, the sustain gets even bigger.