These might be the most misused words in the English language. Lie is an intransitive verb, which means it does not take an object; lay is transitive. The main reason for confusion is that lay is also the past tense of lie. The past tense of the transitive lay is laid. The past participle of lie is lain, and the past participle of lay is laid. The present participle of lie is lying; the present participle of lay is laying.
If all this seems too technical, consider the following sentences as examples of correct usage:
"I often lie down for a nap after lunch."
"Yesterday I lay down for a nap after lunch."
"I have lain here for an hour."
"Please lay the book on the table."
"I laid the book on the table."
"I have laid the book on the table." ...