In one of my other lives I’m a yoga teacher. But because I’m also a fontidious perfectionist, I was horrified to learn that I’ve been misusing lie and lay in my classes.
I had been saying, “Let’s lay down on the floor.” The schoolteachers in my class were undoubtedly thinking, “What is it that she wants us to lay on the floor? Each other?”
So unless you want to create a spectacle of yourself, you lie down on the floor.
Public humiliation. Nothing like it to help one remember the correct usage.
Here’s the short version of how to remember this: you lie down. You also may lie, but that’s your problem. If you’re placing an object, you lay it down.
Grammar Girl and other websites go into detail about present tense, past tense, and past participles. You should go read them. Do that before you lie down.