When the Underground Man decides to attend Zverkov's going away dinner, he takes the money from what should be Apollon's wages.
He talks about having to shine his shoes in private so that Apollon wouldn't see him doing it (since, really, it's Apollon's job).
He has to sneak past Apollon on the way to the dinner, because he still hasn't paid him his wages.
The day after the dinner, the Underground man has Apollon take his apology note and partial repayment to Simonov.
When he worries about Liza showing up, one of his concerns is that Apollon will insult her.
This launches a rather lengthy digression on why the Underground Man hates his servant so much.
According to this tirade, Apollon is the bane of his existence. He is a pedant, a snob, and a tyrant. He also has a lisp, which we've seen is quite despicable to the Underground Man.
The only reason the Underground Man hasn't gotten rid of him is that Apollon is a part of the flat and of his daily life.
The Underground Man fills us in on the details of his little "let's not pay Apollon" experiment. He wants Apollon to be the first to bring up the subject, but instead Apollon just stares at him with disdain until he – the Underground Man – is forced to mention it himself.
By "mention" we mean "fling the wages at Apollon in childish hysteria." But first, he calls Apollon a torturer. In response, Apollon threatens to go to the police, since he is clearly not a torturer.
When Liza shows up, Apollon lets her in and alerts the Underground Man to her presence.
When the Underground Man begs Apollon to get tea for him and Liza, ASAP, Apollon takes his sweet time.