The novel's opening sentences, as Lockwood reflects on his first visit to Wuthering Heights and meeting Heathcliff, are packed with foreshadowing:
1801—I have just returned from a visit to my landlord—the solitary neighbour that I shall be troubled with. This is certainly a beautiful country! In all England, I do not believe that I could have fixed on a situation so completely removed from the stir of society. A perfect misanthropist’s Heaven—and Mr Heathcliff and I are such a suitable pair to divide the desolation between us. A capital fellow!
Some of the irony of this passage is due to the fact that, though Lockwood calls himself a "misanthropist," he's clearly exaggerating—he means something more like "introvert." If he truly hated the company of fellow humans, Lockwood wouldn't have sought out his landlord and neighbor, nor would he have cheerfully judged him "a capital fellow."
The greater irony, though, is the fact that, far from being "a capital fellow," Heathcliff is a misanthropist—though neither Lockwood nor readers know that yet. Despite initial appearances to the contrary, Heathcliff isn't a sociable neighbor with whom to "divide the desolation" of this remote country. In fact, Heathcliff has been a terror to his former neighbors at Thrushcross Grange, but Lockwood will only learn this as Nelly tells him the whole story over the course of the novel. The passage thus foreshadows that, indeed, the Grange and the Heights are incredibly remote from "civilized" society, and in this lonely setting, Heathcliff will be Lockwood's main source of entertainment—though not in the neighborly way he expects, but as the villain of a tale spanning decades.
When Lockwood has dinner at Wuthering Heights for the first time and meets the household, he keeps blundering as he tries to figure out everyone's relationships. He first assumes that Cathy (Linton's widow and Heathcliff's daughter-in-law) must be Heathcliff's wife and then, once corrected, falsely assumes that she's married to Hareton. This is an instance of situational irony because the relationships are not what he, or the reader, expect.
‘Mrs Heathcliff is my daughter-in-law,’ said Heathcliff, corroborating my surmise. He turned, as he spoke, a peculiar look in her direction, a look of hatred unless he has a most perverse set of facial muscles that will not, like those of other people, interpret the language of his soul.
‘Ah, certainly—I see now; you are the favoured possessor of the beneficent fairy,’ I remarked, turning to [Hareton].
Lockwood's blundering throws the reader right in with his own disorientation and confusion; though readers don't know who's who any better than he does, they now understand that this is going to be a complicated story. The "look of hatred" that Heathcliff throws at Cathy reveals generations' worth of pent-up rage, foreshadowing the strife and revenge to come when Nelly tells Lockwood the families' backstory.
The irony in this passage has its humorous side, as the reader pities Lockwood's inability to say anything right; his elevated gentleman's language ("the favoured possessor of the beneficent fairy") doesn't match the rural Yorkshire setting or the animosity-filled family atmosphere. Besides tasting the palpable awkwardness, readers are also primed to pay close attention to the narrative in order to untangle these relationships—and to understand how they grew so embittered.
Nelly describes how Heathcliff came to be the owner of Wuthering Heights after Hindley Earnshaw mortgaged it away to pay off the debts he accumulated by gambling with Heathcliff. This is an instance of situational irony, given everything readers would expect about the importance of inheritance in old, respected families like the Earnshaws.
The guest was now the master of Wuthering Heights [...] Earnshaw had mortgaged every yard of land he owned for cash to supply his mania for gaming: and he, Heathcliff, was the mortgagee. In that manner, Hareton, who should now be the first gentleman in the neighbourhood, was reduced to a state of complete dependence on his father’s inveterate enemy; and lives in his own house as a servant deprived of the advantage of wages, and quite unable to right himself, because of his friendlessness, and his ignorance that he has been wronged.
Recall that when readers are introduced to Wuthering Heights, Lockwood notices the name of family ancestor "Hareton Earnshaw" above the door. Later, Hindley's son Hareton is named after his 16th-century forebear—a plain indication that Wuthering Heights is meant to be passed down to future generations of Earnshaws. Given the significance of inheritance in this society, then, it's an especially grievous irony that the current Hareton Earnshaw has been swindled out of what's rightfully his by Heathcliff—his father's poor, adopted orphan brother with no natural claim on the Earnshaw heritage.
This circumstance is also meant to show how truly dissipated Hindley became: allowing his son's inheritance to be gambled away is a shameful dereliction of duty. And after Hindley dies, young Hareton has no idea what he's lost because Heathcliff raises him the way Hindley raised Heathcliff —that is, like a servant, isolated and uneducated. So, even though Heathcliff is the one who abuses and degrades Hareton, he does so in retaliation for the way Hindley treated him, making Hindley responsible for the Earnshaws' downfall twice over.