The verb lay means ‘to put something down carefully in a flat position’. It must have an object. It is a regular verb, but note the spelling of the past simple and -ed form: laid not layed:
Shall I lay the tray on the bed?
A wonderful wooden floor has been laid in the dining room.
Not: … floor has been layed …
Lie is a verb which means ‘to be in or put yourself into a flat position’. It is an irregular verb and it doesn’t take an object. The -ing form is lying and the past simple is lay. The -ed form, lain, is very formal and is rarely used:
I love to lie on a beach and read.
She lay on the bed and gazed at the ceiling, daydreaming.
The dog was lying by the gate waiting for me to come home.
Lie can also mean ‘say something which is not true’. In this case, it is a regular verb:
I lied to my teacher about my homework.
lay (put something down)
lie (be horizontal)
lie (say something that is not true)
We don’t use lay to talk about being in a flat position. Lay must have an object:
My mother hates when the cat lies on our beds.
Not: … when the cat lays on our beds …
The past form of lie is lay:
I lay on the grass and watched a plane fly overhead.