A lot of people, even native speakers, get these confused.
To lay - a transitive verb. You have to lay something. The chicked laid an egg, go lay your coat on the chair over there, the mason is laying tile.
To lie - an intranstive verb, what the person does herself. I am goig to go lie down for a bit. I lay on the couch all day watching terrible movies. I was just lying under the tree, watching the clouds.
The confusion comes because "lay" appears as a form of both verbs.
It's the same with "to set" and "to sit" - the first is transitive. Set your keys on the counter, I had to set the box down because it was too heavy. If you can keep the difference between sit and set in your mind, and then think that lie is like sit, and lay is like set (keep the i's together), it may help.
Could someone please explain the difference between the verbs lay (laid, laid) and lie (lay, lain). I don't know how to use them correctly.
First of all they are different in meaning. The verb to lay is a synonym of the verb to put. The only problem is that the first form of the verb to lay and the second form of the verb to lie is the same. While using these forms you shouldn't mix them. You can even use both in one sentence.
e.g. At first he laid the table and then lay on the sofa to have a short rest.