Lie (to fib): lie, lied, lied. (You lie, you lied, you have lied.)
Lay (to put down): lay, laid, laid. (I lay the book down, I laid it down, I had laid it down.)
Lie (to recline): lie, lay, lain. (I lie on the hammock, I lay on the bed, I had lain on the cold, wet ground.)
Pretty simple, right? The first (to lie) is a simple verb. I lie all the time. I have lied, I do lie, I will lie. The second (to put down) is a transitive verb, meaning it conveys an action from one thing to another. I lay the book down, I will lay it down, and I have laid it down—it conveys what I do to the book. The final one is the funky one of the three, and it helps to memorize the convention. I currently lie on my bed, but yesterday I lay on the bed.