lie (+ phrase of place) / lay (+ object)
Perhaps the easiest way to remember the difference, Antonio, is that lay is a transitive verb which needs an object to complete its meaning and lie is an intransitive verb which functions without an object and is followed normally by a phrase of place.
First, see how the words look in the present and the past tense.
lie he lies..., he is lying... he lay..., he was lying..., he has lain...
lay she lays, she is laying he laid, he was laying, he has laid
Now compare the following:
lay ( + object) She laid the baby on the bed in order to change its nappy.
lie ( + phrase of place) She was lying asleep on the sofa when her husband arrived home.
lay ( + object) Can you lay the table for me please? Lunch is ready.
lie ( + phrase of place) I told her not to lie out in the sun, but she must have lain there for at least an hour for her back was very sunburnt.
lay ( + object) I had never laid carpets before, but I was determined to have a go.
lie ( + phrase of place) When I looked out of the aircraft window, I could see that London lay beneath us.
lay ( + object) His lawyer will lay great emphasis on his state of mind when the murder was committed and claim that it was manslaughter, not murder.
lie ( + phrase of place) None of us knows what lies ahead, but you must try to take a grip on your life and decide where your future lies.