。
She lay down on the floor and started reading.
Literal
She [topic-は] floor [on-に] lay-down [then-て] reading [object-を] began.
横たわる (よこたわる, 'to lie down, to recline') is the intransitive verb for assuming a horizontal position. 読書 (どくしょ, 'reading') is the formal noun for the activity of reading. The て-form connects lying down with beginning to read — a comfortable domestic scene.