I lay down my backpack in the hallway when I get home.
Notice that the transitive verb (the one you do to an object) is more regular than the intransitive verb (the one you do to yourself). Lay adds -ing and -ed (with a spelling change). Lie adds -ing, but changes to lay and lain.
I lie down on my bed when I am tired.
I am lying down on my bed right now.
I lay down on my bed yesterday.
In the past I have lain down on my bed.
I lay my backpack down in the hall.
I am laying my backpack down.
Yesterday I laid my backpack down.
In the past I have laid my back pack down.
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