You don't plug it into your computer, you plug it into one of the other Ethernet ports on your router.
To be blunt doing this task right is a little beyond your knowledge.
Sure you can just plug it in and use the included services, but now your entire camera system is very vulnerable to hackers and they can see your cameras.
To do this right you need to go into the dvr configurations, change default username and password, use a non-standard port number, disable ddns/telnet/upnp, assign a static ip address, forward the port on the router, and setup your own ddns service (instead of relying on the dvr companies).