Use lay to mean put down, or place. And it requires a direct object, the thing that is put or placed. Hens lay eggs. Bricklayers lay bricks. Healers lay hands upon the infirm. In every case, lay has an object–eggs, bricks, hands. In other tenses, lay takes these forms: Hens laid eggs last week; Hens are laying eggs faster than ever; Hens had laid the eggs before the sun rose.
Lie means recline, or occupy a location. It does not take an object, because the subject can accomplish those things alone. The idle rich lie on beaches. The restless lie awake. The faithful will lie down in green pastures. Governors Island lies off Manhattan. Sleeping dogs just lie. The rich, the restless, the faithful, the island and the dogs need no help–no object to complete their actions. They simply lie there. And in other tenses, lie takes these forms: The rich are lying on the beach despite the shaky economy; The rich had lain on the beach before moving to the slopes.
Confusion arises because the past tense of lie also happens to be lay, playing a different role: The idle rich lay on the beach yesterday.
Source: The New York Times Manual of Style and Usage, 1999, by The New York Times Company.