“Lay” (present tense) implies an agent acting on something, and it means “to put, place, or prepare.” Its other forms are “laying,” “laid” (past tense), and “laid” (with “has,” “have,” or “had,” usually implying a past event that continues into the present):

I lay the nugget in the empty pan. (Present tense—the nugget was put there by an agent.)

They were laid there centuries ago. (Past tense—they were placed by an agent.)

“Lie” (present tense) means “to recline” or “to be situated,” and its other forms are “lying,” “lay” (past tense), and “lain” (with “has,” “have,” or “had,” usually implying a past event that continues into the present):

This tomb has lain undisturbed for thousands of years. (Used with the helper “has”—it has been situated.)

During field camp in the Connecticut Valley last year, he lay down next to an eight-foot black rat snake. (Past tense—he reclined, albeit briefly, to be sure.)