When I was a boy, I used to lie on my back on the grass and gaze at the white clouds.
Literal
I [topic-は] boy [possessive-の] time often grass [possessive-の] top [on-に] face-up-[manner-に] lay-down-[sequential-て], white clouds [object-を] gazed [nostalgic-past-ものだった].
あお向けに ('face up, on one's back') marks the posture of lying down. 仰向け is the kanji form — literally 'facing upward.' The に marks manner. 寝ころぶ is a variant of 寝転ぶ ('to lie down, sprawl') with the same meaning. The ~ものだった ending bathes the recollection in the warm glow of nostalgia.