The correct form depends on whether you're using the present or past tense. Use "lie down" when someone or something is reclining (present tense), and "lay down" when you're placing something somewhere or referring to the past tense of "lie."
For the present tense:
- Use "lie down" when someone or something is reclining without an object (intransitive). Example: "I need to lie down for a nap."
- Use "lay down" when placing something somewhere (transitive). Example: "Please lay down your weapons."
For the past tense:
- "Lie" becomes "lay" in the past tense. Example: "Yesterday, I lay down for a nap."
- "Lay" becomes "laid" in the past tense. Example: "She laid down the book on the table."
The confusion often stems from "lay" being both the present tense of one verb and the past tense of another. Remember: if there's a direct object receiving the action, use forms of "lay."