Students are selected for scholarships by means of an open, national competition.

by 是介词，表示"通过某种方式或手段"。 means 是名词，意思是"方法、手段"，常与介词 by 搭配使用。 of 是介词，在这里与 means 构成固定搭配，表示"通过...的方式"。 by means of 是一个固定短语，意思是"通过...的方式"或"借助...的手段"。