Linking his Linux to my Mac


My computer is a Mac desktop running OS10.6.8. Our internet server is Verizon DSL with a 7500 router. We bought a used desktop computer that has Linux Mint. We installeda Lynksis adapter on his computer and have a good signal.
However, we can't connect to a server. I assume that his Linux needs to be linked to my Mac, but I don't know how. Any help?