It apparently communicates with the stars in the night sky by flashing the red core at the center of its body. If parts of its body are torn, this Pokémon simply regenerates the missing pieces and limbs.
(From Bulbapedia) Staryu is a golden-brown sea star-like Pokémon with five appendages. These appendages surround an exterior organ called the core, which is held in place by a golden ring looped around Staryu's left "leg". If any of Staryu's appendages are lost, it can grow them back with ease provided the core is still intact. The core resembles a red jewel and is similar to a madreporite. Staryu is a natural prey of some species of Pokémon, including Lumineon. However, due to its regenerative abilities, being preyed upon does not negatively affect it.
When the sun goes down, the core glows its brightest. Many will float from the seafloor to the surface and align themselves with stars of the night sky as their core flickers, displaying a connection with the celestial bodies of space.
(From Bulbapedia) Staryu's design is based on a starfish, likely a common starfish. Conceptually, it appears to be a pun on a literal star, as Staryu is rumored to be extraterrestrial in nature.
The large gemstone attached to its body is held on by a bracket, similar to a ring mount. Additionally, although Staryu's gem seemingly does not display it, the concept of asterism is worth mentioning in terms of Staryu's possible design basis, especially since Staryu's is a cabochon gem. If this was indeed inspiration for its design, then Staryu's gem is perhaps a star-ruby.
(From Bulbapedia) Staryu is derived from star (referring to its shape) and yu (possible corruption of you, in opposition to the mie in Starmie). Yu is also the Chinese word for fish (魚).