I spread out a newspaper and draped it over my dead child.

Literal

Newspaper [object-を] spread-[and-て] deceased-child [on-に] covered-over.

A dark and sparse sentence from narrative fiction. 亡子 (ぼうし) is a rare, literary noun specifically meaning 'one's deceased child' — a word you'd meet in literature rather than conversation. 覆いかぶせる is a compound verb 覆う ('cover') + かぶせる ('put over, place over the top'), meaning 'to drape over, lay atop.' The restraint of the vocabulary mirrors the grim content.