I'm not sure the narrator started out with a plan, but this is how the plan unfolded:
The narrator admits he was overly nice to the old man in the week before he killed him, in order to allay suspicion, "I was never kinder to the old man than during the whole week before I killed him." The next step was that the narrator watched the old man every night while he was sleeping. He snuck into the old man's room just around midnight to try to sneak a glance at the eye. "And this I did for seven long nights - every night just at midnight - but I found the eye always closed; and so it was impossible to do the work; for it was not the old man who vexed me, but his Evil Eye."
The next step was that he acted perfectly normally during the day, speaking to the old man and asking him mundane questions so the old man would not suspect anything was amiss, "So you see he would have been a very profound old man, indeed, to suspect that every night,...
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