Large language models (LLMs) have demonstrated impressive capabilities in general scenarios, exhibiting a level of aptitude that approaches, in some aspects even surpasses, human-level intelligence. Among their numerous skills, the translation abilities of LLMs have received considerable attention. Compared to typical machine translation that focuses solely on source-to-target mapping, LLM-based translation can potentially mimic the human translation process, which might take preparatory steps to ensure high-quality translation. This work explores this possibility by proposing the MAPS framework, which stands for Multi-Aspect Prompting and Selection. Specifically, we enable LLMs first to analyze the given source sentence and induce three aspects of translation-related knowledge (keywords, topics, and relevant demonstrations) to guide the final translation process. Moreover, we employ a selection mechanism based on quality estimation to filter out noisy and unhelpful knowledge. Both automatic (3 LLMs × 11 directions × 2 automatic metrics) and human evaluation (preference study and MQM) demonstrate the effectiveness of MAPS. Further analysis shows that by mimicking the human translation process, MAPS reduces various translation errors such as hallucination, ambiguity, mistranslation, awkward style, untranslated text, and omission. Source code is available at https://github.com/zwhe99/MAPS-mt.