Even though I know this grammar rule, I still always double-check in my trusty, well-worn, AP Stylebook.
Simplified: lay is for objects, lie is to recline. You lay an object on a table. You lie down.
“The action word is lay,” according to the AP Stylebook. “It takes a direct object. Laid is the form for its past tense and its past participle. Its present participle is laying. Lie indicates a state of reclining along a horizontal plane. It does not take a direct object. Its past tense is lay. Its past participle is lying.”
The Stylebook entry goes on to make a few examples.
Present or future tenses:
I will lay the book on the table. The prosecutor tried to lay the blame on him.
He lies on the beach all day. I will lie down.
I laid the book on the table. The prosecutor has laid the blame on him.
He has lain on the beach all day. I lay down. I have lain down.
I am laying the book on the table. The prosecutor is laying the blame on him. He is lying on the beach. I am laying down.
Clear as mud?