Here’s how to keep them straight.
Lay is a transitive verb—it takes an object.
Ex: She lays down her pen and stands up.
Ex: He laid the newspaper on the table.
Ex: The table was laid for four.
Lie is an intransitive verb and cannot take an object.
Ex: She often lies down after lunch.
Ex: When I lay down, I fell asleep.
Ex: The rubbish had lain there a week.
Ex: I was lying in bed when he called.
But bear in mind that lay is often an expressive way to say “lie” and has a charmed existence in certain uses. Don’t most dog owners at one time or another say Lay down! to their dogs? How many golfers play it as it lays? How many employers exhort their workers with Let’s not lay down on the job? What if Bob Dylan, in a fit of zeal for correctness, had written “Lie, Lady, Lie/Lie across my big brass bed?” Somehow it’s hard to imagine the lady sticking around.
Source: § 192. lay / lie. 3. Word Choice. The American Heritage Book of English Usage. 1996