No doubt, these words are among the most problematic for a lot of people, myself included! Pop music only serves to make things worse; just as groups like The Beatles singing "She's got a ticket to ride, but she don't care" doesn't help learners with the third person singular verb, Eric Clapton's "Lay down Sally" and Bob Dylan's "Lay lady lay" don't help us with lay and lie.
What not many people realise, however, is that don't was a standard contracted form of does not until the early 20th century, and is still being used today in some parts of Britain by the British (not by foreigners in case you were thinking that) in spite of it being grammatically incorrect. Since when does colloquialism bother about grammar, right?
Similarly lay being used intransitively (I'll explain shortly) instead of lie is frowned upon, but, according to Merriam-Webster, has been used since the 14th century, and was accepted until the late 1700s, when attempts were made to correct the misuse. Just as don't for third person is being used colloquially now, so is lay instead of lie.
All that aside, you're here to learn the right forms, correct? So, let us take a look.
This is a transitive verb, meaning it needs an object: we lay someone or something down, we can lay a table, and birds lay eggs.
Remember that both Dylan & Clapton were using it 'incorrectly'.
This is an intransitive verb, meaning it doesn't need an object: we lie on the bed, Sally lies on the grass next to me. For other meanings, click on the heading above.
We also have the phrasal verbs 'lie in - lay in - lain in' meaning to stay in bed for longer than usual, and 'lie down - lay down - lain down' meaning the same as lie. So, we can say we lie on the bed or we lie down on the bed.
LIE - LIED - LIED
This is a regular verb, meaning to say something that is not true: she's always lying about her age, why did you lie to me?