Lie is an intransitive verb (one that does not take an object), meaning "to recline." Its principal parts are lie (base form), lay (past tense), lain (past participal), and lying (present participle).
[Lie meaning "to tell an untruth" uses lied for both the past tense and past participle, with lying as the present participle.]
Lay is a transitive verb (one that takes an object), meaning "to put" or "to place." Its principal parts are lay (base form), laid (past tense), laid (past participle), and laying (present participle).
The two words have different meanings and are not interchangeable. Although lay also serves as the past tense of lie (to recline) – as in, "He lay down for a nap an hour ago" – lay (or laying) may not otherwise be used to denote reclining. It is not correct to say or write, "I will lay down for nap" or "He is laying down for a nap." The misuse of lay or laying in the sense of "to recline" (which requires lie or lying) is the most common error involving the confusion of these two words.
> Once you lay (put or place) a book on the desk, it is lying (reclining, resting) there, not laying there.
> When you go to Bermuda for your vacation, you spend your time lying (not laying) on the beach (unless, of course, you are engaged in sexual activity and are, in the vernacular, laying someone on the beach).
> You lie down on the sofa to watch TV and spend the entire evening lying there; you do not lay down on the sofa to watch TV and spend the entire evening laying there.
> If you see something lying on the ground, it is just resting there; if you see something laying on the ground, it must be doing something else, such as laying eggs.