Lay is a verb, meaning to put something down, sometimes very carefully 'go and lay the table'
Laid is the past tense - 'I laid the table at breakfast'
Laid is the past simple tense (words often ending in -ed, but not this case) - 'the builder laid the first brick' NOT layed
Lie is an irregular verb, meaning to be horizontal - 'I love to lie on the beach and read''
Lay is the past tense - 'I lay on the sofa all day yesterday'
Lain is the past simple tense (words often ending in -ed, again not in this case) - 'he had lain on the sofa' NOT Lied
** Lie also means to tell an untruth, to deceive.
Really hope that's helped.