Lay is the past tense form of lie.
Laid is the past tense of lay.
- I will lay my head on the pillow.
(lay something/lay my head) - I like to lie on the sofa for my naps.
The dog lay down and went to sleep.
(past tense of lie/lay) - They laid the picnic out on the cloth.
(past tense of lay/laid)
More help with irregular verbs.