This one's easy. In most cases:|
Lay requires an object.
You always lay something (or someone, if that makes it easier for you to remember...)
"lay down on the bed"
but you do
"lay your head down on the pillow."
"lie down on the bed"
but you don't
"lie your head down on the pillow."
(You can also lie about the object of the word lay but that use isn't as confusing.)