In the strictest grammatical sense, 'lie' is
an intransitive verb, whereas 'lay' is transitive. Conceptually, 'lie' is
something you do to yourself, and 'lay' is something you do to something/someone
else.
Word
Example
lie
You look tired. Lie down and rest.
lay
Lay down the keyboard and step away from the
computer!
The past tense,
however, gives many people fits. The past tense of 'lie' is 'lay', and the past
tense of 'lay' is 'laid'.