Whoever wrote the grammatical rules for lay, lie, laid, lain and lied ought to be shot. Then he should be shot a second and third time...just to be sure. In real life, most people are not gonna call you on this error because they're just as confused. I have never found a simple and clear explanation of the rule that didn't devolve into grammatical jargon. The only way to remember this rule is sheer memorization. I'll try to help you by providing example sentences that aren't as forgettable as the typical, "He lay/lie/laid on the floor." Yeah, thanks Captain Grammar. Now I know why you're a goddamn grammarian and not an actual writer.
to lay (to place an object in a horizontal position)
Vader leads Luke up to the throne and lays his son's lightsaber on the Emperor's orthopedic chair. (present tense)
Vader lead Luke up to the throne and laid his son's lightsaber on the Emperor's chair. (past tense)
Luke was weaponless becuase Vader had laid his lightsaber on the Emperor's chair. "Thanks a lot, dad," he thought grimly. (past participle)
to lie (to be in a horizontal position)
"Lie down in the cargo hold and keep quiet," Han told Chewie before the Stormtroopers boarded the ship. (the sentence in quotes is in the present tense)
Chewie lay down in the cramped space. (past tense)
The Stormtroopers searched the ship, but never found Han and his passengers who had lain in the hold for hours. (part participle)
to lie (to prevaricate, to speak falsely)
As a smuggler, Han often lies to space ports about his destination and cargo. (present tense)
Han lied about his cargo in order to land the Tyderian Shuttle safely on Endor. (past tense)
Bottom line: If a subject is acting on another object, use "to lay." That's why we have the sexual meaning of lay or laid in reference to "She got laid last night." It's a subject acting on (laying) another object (hopefully another person, you pervert). Oh, sorry for the passive tense of the "she got laid" example, but chalk that up to common usage.