How can I play LAN games online?

I wanna play games with my cousin somewhere else. I don't wanna go online for Multiplayer(for unmentionable reasons). Can you please tell me what i can do to play with him. And also we have 2 PCs in our place that's hooked up together via wired connection. Can we play together with my brother? And I've heard of hamachi. Will it solve the problem?