Please give me a pillow and blanket.

Literal

Pillow [and-と] blanket [object-を] give-[please-下さい].

[noun]をください is the direct-object form of polite request — 'please give me X.' Distinct from [verb]てください ('please do X for me'), this asks for the items themselves rather than for someone to perform a fetching action. The conjunctive と links pillow and blanket as a single request unit.