In "The Cask of Amontillado," how does Montresor lure Fortunato farther and farther into the catacombs?

Montresor lures Fortunato further and further into the catacombs through appeals to his vanity, through reverse psychology, through flattery and through keeping him drunk. 

Montresor begins to spring his trap even before they enter the catacombs and will continue it as they go deeper and deeper.

Montresor first pricks Fortunato's vanity and plays on his rivalry with Luchresi by telling him about the amontillado, and then saying:

"'I am on my way to Luchresi. If any one has a critical turn it is he. He will tell me—'"

Fortunato responds as expected: "'Luchresi cannot tell Amontillado from Sherry.'"

Montresor then uses reverse psychology, insisting Fortunato is too busy to taste the amontillado (and also mentions his rival again):

"'My friend, no; I will not impose upon your good nature. I perceive you have an engagement. Luchresi—'"

Fortunato again responds on cue: "'I have no engagement;—come."

Montressor continues to use reverse psychology, flattery and Luchresi within the catacombs. When they are deep inside, Fortunato, sensitive to the nitre (mold) and the damp, has a coughing fit. Montresor responds:

"'Come,' I said, with decision, 'we will go back; your health is precious. You are rich, respected, admired, beloved; you are happy, as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill, and I cannot be responsible. Besides, there is Luchresi—'"

Again, this works like a charm (one wonders what would have happened if it didn't): 

"'Enough,' he [Fortunato] said; 'the cough's a mere nothing; it will not kill me. I shall not die of a cough.'"

This gives the well-prepared Montresor the opportunity to further disable his victim by offering him more to drink:

"'True—true,' I replied; 'and, indeed, I had no intention of alarming you unnecessarily—but you should use all proper caution. A draught of this Medoc will defend us from the damps.'

Here I knocked off the neck of a bottle which I drew from a long row of its fellows that lay upon the mould.

'Drink,' I said, presenting him the wine."

Fortunato is already quite tipsy, as we know because he "leers" and the bells on his cap jingle as if he is unsteady. At this point they are so far into the catacombs that Montresor has won, all by manipulating his friend into insisting on walking into the trap.