The difference between and correct usage of “lay” and “lie”

If you exclude the meaning “to tell an untruth” and just focus on the setting/reclining meaning of lay and lie, then the important distinction is that layrequires a direct object and lie does not. So you lie down on the sofa (no direct object), but you lay the book down on the table (the book is the direct object).

This is in the present tense, where you are talking about doing something now: you lie down on the sofa, and you lay down a book.”