How do I ask "Can you wash your clothes at the hotel?"
To translate directly:


  "Can you wash your clothes at the hotel?"
  
  你可以在宾馆洗你的衣服(clothes)吗?


Not sure if it is really what you want. But if you are asking the hotel staff whether they help you wash your clothes, then it should be:


  "Do you provide laundry service?"
  
  你有提供洗衣服务(service)吗?


The basic order of a Chinese sentence is usually in the form of subject-verb-object arrangement. From the two sentences above, 你 is the subject, 洗 and 提供 are the verbs, 衣服 and 洗衣服务 are the objects. Please refer to this article for more examples on the Chinese grammar.