How do scientist study the moons interior?

They must infer its components and processes from the rocks they find on the surface, as well as other things they know about the solar system from both meteorites as well as the materials of the Earth. They study the chemical and mineral composition and structure of lunar rocks, and this can tell them what the interior looks like based on what they know about different mineral densities and melting points, etc., and how that fits into the current understanding of how the moon formed about 4.5 billion years ago.