Software

Is the camera currently using the PC for control and storage? Or is this a seperate unit that has the ability to stream via a video out port?

Or chose which Video feed to access remotely?

This is the first question that you need to ask and then set about configuring the system to support your needs which could be very involved or quite simple depending on exactly what it is that you wish to do. A simple off site storage in case of robbery is easy to achieve but to look in real time through a specific camera is much more involved.

Col

Yes, It is possible, there are DVR unit with network function. Such as this 8 channel one.

http://www.dvrsecuritylab.com/avc785d-8-channel-w-dvd-recorder-usb-remote-security-camera-cctv-video-surveillance-c-251-p-1-pr-16144.html

you just connect the DVR with an Ethernet cable to your network (router) and then setup the DVR so that it has a IP address. For a router, you will need to allow port forwarding to access over the internet.