LAY is an action, a thing you do to something else. It means ‘put’ or ‘place.’ That makes it a transitive verb--a verb that has to have a direct object. You lay your coat on the bed, lay yourself down to sleep, or lay the blame somewhere--the coat, self, and blame are the direct objects. You can’t lay on the couch. LAY is also slang for having sex--and still requires a direct object.

Simple present tense: lay(s). The boy lays his book down. We lay our guests' coats on the bed. The pavers lay asphalt in twelve-foot sections.
Simple past tense: laid. The sheriff laid the print-out on the dashboard. Marie laid down the flyswatter. Jared laid plenty of girls--in his imagination.
Simple future tense: will lay. He’ll lay the baby in her crib after she falls asleep. We will lay miles of concrete during the project.
Present perfect tense: has/have laid. She has laid her map on the counter. That slut has laid every guy in town. The army has laid down their arms. We have laid our terms before the trustees.
Past perfect tense: had laid. Sir Walter had laid his cloak over the puddle. I had laid my glasses somewhere.
Future perfect tense: will have laid. The farmer’s hens will have laid a million eggs by July. The company will have laid enough pipe to circle the globe.
Present progressive tense (for an action which is ongoing): am/is/are laying. Shelly is laying out napkins. I’m laying bricks this summer. You’re laying bratwurst on sourdough?
Past progressive tense (for an action which is ongoing): was/were laying. Joe was laying tile. You were laying cheerleaders?
Future progressive tense: will be laying. Murray will be laying carpet until Bob comes back to work. If he tells the truth, James will be laying a lot of guilt at his ex’s feet.
Present perfect progressive tense: has/have been laying. Union workers have been laying the groundwork for the agreement. The whole frat has been laying campus cuties. Father Anselm has been laying prayer books on the pews.
Past perfect progressive tense: had been laying. The drag racer had been laying rubber since he was sixteen. Gretel had been laying breadcrumbs to mark the way.
Future perfect progressive tense: will have been laying. By fall, I will have been laying my life on the line for two years. Sharon will have been laying rose petals most of the morning.
Present participle, used as an adjective: laying. The man laying sewer pipes wipes his brow. We averted our eyes from the homeless guy laying out his blankets.
Past participle, used as an adjective: laid. Laid in rows, the bodies had begun to rot. Lint covered the towels laid in anticipation of my visit.

LIE is a situation, a way a thing can exist. It means ‘rest on a surface’ or ‘be situated.’ That makes it an intransitive verb--a verb that can’t have a direct object. You lie on the couch, or the goal lies within reach. The past tense of lie is lay, which is undoubtedly where the confusion comes from.

Simple present: lie(s). Antoine lies in wait. I lie on the sofa. You lie there like a dead fish. The backpack lies by the door, daring me to leave.
Simple past tense: lay. The seeds lay dormant all winter. We lay in bed that night, not speaking. No, you lay in the hammock, remember?
Simple future tense: will lie. The catatonic patient will lie motionless for hours. Will you lie in bed all day? The books will lie there until somebody picks them up.
Present perfect tense: has/have lain. A clue has lain in the tomb for centuries. She has lain in the darkened room, seeing only her children. Cows have always lain in clover.
Past perfect tense: had lain. The key had lain there unseen. He’d lain shivering through the night. The answer had lain in Ed’s files all along.
Future perfect tense: will have lain. The rocks will have lain undisturbed until excavation begins. Soon the volcano will have lain dormant twenty years, but we won’t rebuild.
Present progressive tense (for an action which is ongoing): lying. The baby is lying in her crib. We’re lying on the sand. I’m lying there exhausted, ignoring the sirens.
Past progressive tense (for a past action which is ongoing): was lying. While his son mowed, Larry was lying on the porch listening to the game. The sniper was lying in wait until an officer came into range.
Future progressive tense (for a future action which is ongoing): will be lying. The tickets will be lying right here. This mess will be lying here waiting for you.
Present perfect progressive tense: has/have been lying. The fossil has been lying unnoticed. The catfish has been lying on the river bottom. Gold nuggets have been lying near the mother lode.
Past perfect progressive tense: had been lying. Bits of bone had been lying among the cinders. Miriam had been lying in the hospital, bored out of her mind.
Future perfect progressive tense: will have been lying. The wedding dress will have been lying on Mandy’s bed for a year next Tuesday.
Present participle, used as an adjective: lying. Lying inert, Sandy’s cow could not be moved. The boy lying beneath the trees could be hurt.
Past participle, used as an adjective: lain. The tenor picks up the roses lain center stage by his fans. We walked right into the trap lain for us.

LIE is also to state an untruth, to deceive. It is an intransitive verb--no direct object--but may have an indirect object, the person who is being lied to, or the person or thing being lied for. People don't often make mistakes with this one, though.

Note that there is no word layed.

Maryn, providing yet another public service (guffaw)