* Couché is used for a male subject.
* Couchée is used for a female subject.
Here are some examples:
* Le chat est couché sur le canapé. (The cat is lying down on the couch.)
* La petite fille est couchée dans son lit. (The little girl is lying down in her bed.)
You can also use the verb s'allonger which means "to lie down".
* Je m'allonge sur le gazon. (I am lying down on the grass.)
* Il s'est allongé sur le sol. (He lay down on the ground.)
The choice between couché(e) and s'allonger depends on the context and the desired nuance.