How does Fortunato become locked in the chains so easily?
Edgar Allan Poe, the creator of the story, has made it easy for Montresor to chain Fortunato to the granite wall and easy to build a stone wall to conceal him. Here is how Montresor describes the crypt and the chains.
Within the wall thus exposed by the displacing of the bones, we perceived a still interior crypt or recess, in depth about four feet, in width three, in height six or seven...A moment more and I had fettered him to the granite. In its surface were two iron staples, distant from each other about two feet, horizontally. From one of these depended a short chain, from the other a padlock.
Fortunato is in a "crypt or recess" only four feet deep and three feet wide. Its height is only about the same height as a man. Montresor only has to build a small wall of stones in order to conceal his victim. This enables Poe to finish the story quickly. It also explains how Montresor is able to build a stone wall when he cannot have had much experience. The stone wall only has to be three feet wide and six or seven feet high.
The chains must have been there for more than a century. The iron staples holding the chains to the rock wall behind Fortunato are only about two feet apart, and one chain is described as short. The padlock may be attached to a much shorter chain. It is an old-fashioned padlock that has to be locked with a key and not snapped shut like our modern padlocks. Fortunato would be pinned against the rock wall behind him. It should only take a matter of seconds to wrap the short chain around his waist and lock the padlock at the tightest link so that the victim would have hardly any freedom of movement.
Poe has specified that the crypt or recess is about four feet deep. This depth is necessary to prevent Fortunato from reaching out and pushing against the stone wall, either while Montresor is building it or after Montresor leaves and the mortar is still wet. Fortunato's arms would only be three feet long at most. He might try to touch the masonry but find it frustratingly just out of reach.
Poe has made Montresor's work as easy as possible. Since Fortunato is drunk, it is understandable that Montresor could wrap one short chain around his waist with one hand and insert the padlock with the other before his victim realized what was happening.
The reader understands that Montresor wants to kill Fortunato but does not understand how Montresor intends to do it until he has chained his victim to the rock wall and has shut the padlock. At this point Poe achieves the "single effect" he intended. After this effect of horror is achieved, Poe would want to finish his story as quickly as possible. No doubt this explains why the crypt or recess is so small--only about three feet wide and six or seven feet high. Montresor can finish the wall-building quickly and describe the whole process in only a few sentences.
I hastened to make an end of my labour. I forced the last stone into its position; I plastered it up. Against the new masonry I re-erected the old rampart of bones. For the half of a century no mortal has disturbed them. In pace requiescat!
One of the biggest reason has to do with the fact that Fortunato is very, very drunk. The narrator makes sure to have him drink as much wine as possible as they progress along the passageways. Of course Fortunato had been drinking all day given that it was during the "supreme madness of the carnival season." The narrator has also directed the attention of Fortunato to the Amontillado, something so rare and wonderful that Fortunato can think of nothing else. He cannot possibly suspect that there is a chance of anything untoward happening as they progress into the vaults.
Because Fortunato is so focused on finding the wine, it even takes him a moment to become alarmed after he has been chained to the wall. As the narrator describes, he was "bewildered" to find himself at the end of the tunnel and it only took a moment to chain him to the granite wall.