What is meant by "he lived a year in a minute"?
As Rainsford was working on making the trap, it seemed he worked quickly, frantically, and exhaustingly spending much exertion. I imagine, if he could track his output in the short amount of time he had to make the trap, it would have been comparable to the amount of work his body normally does over days, weeks, or months. Then, to sit in anticipation after unloading all of that work probably felt like forever. He knew he was racing against the time at which Zaroff would again show up. He did not know how long that would take. Once his task was done, it should seem that any moment it would be acceptable for Zaroff to approach... but it took a while - that little while felt like forever to him.
I assume that you have heard (probably many times) the saying that "time flies when you're having fun." Well, this is sort of the opposite. It is meant to show how nervous and scared Sanger Rainsford was at this point in the story.
At this point, Rainsford has made his Burmese Tiger Trap and he's really anxious, hoping that Zaroff will fall in. It really is a matter of life and death for him. As a way to show this, the author says that time is moving really slowly for Rainsford.
Think about sometime that you've been scared or nervous. How did time feel to you at that point?