This is a biggie for me. I never get lay versus lie right, no matter how much I try. I've resorted to letting Microsoft Word figure it out for me.
Here's what I found on the subject, from my trusty 'English Grammar and Composition' book that I got when I was younger.
The verb lie means 'to rest' or 'to recline,' 'to remain in a lying position.' It's principal parts are lie, lying, lay, (have) lain. The verb lie never takes an object.
The verb lay means 'to put' or 'to place (something).' Its principal parts are lay, laying, laid, (have) laid. These forms may have objects (receivers of the action).
Infinitive present participle past past participle
lie (to rest) lying lay (have) lain
lay (to put) laying laid (have) laid
Examples of lie, meaning 'to rest' or 'to recline.'
Occasionally I lie down.
The letter is lying on the desk.
Yesterday Bennett lay on the sand.
How long have you lain here?
Examples of lay, meaning 'to put' or 'to place (something)':
Lay the boards down.
I was laying the letter on the desk.
Yesterday Bennett laid these towels on the sand.
Have you laid your work aside?
I hope that helps.
Have a great day!
Reference: 'English Grammar and Composition' by John Warriner, Mary Whitten, and Francis Griffith. Harcourt Brace Jovanovich, New York, 1973.