Shall I make dinner?

Literal

Dinner [object-を] prepare-[polite-ましょうか].

~ましょうか ('shall I?') is the offer-to-help form, a polite volitional softened into a question. 用意する ('to prepare, arrange, make ready') is a standard suru-verb for preparation — similar to 準備する but slightly more everyday. A gentle, helpful offer common in polite exchanges.