In this paper we present a step-by-step approach to long-form text translation, drawing on established processes in translation studies. Instead of viewing machine translation as a single, monolithic task, we propose a framework that engages language models in a multi-turn interaction, encompassing pre-translation research, drafting, refining, and proofreading, resulting in progressively improved translations. Extensive automatic evaluations using Gemini 1.5 Pro across ten language pairs show that translating step-by-step yields large translation quality improvements over conventional zero-shot prompting approaches and earlier human-like baseline strategies, resulting in state-of-the-art results on WMT2024.