To run a network camara does that cost anything other then the camara itself?

Answer 1

The basic answer is NO. The camera itself and the setup time are all that you need.

The rest of the answer is there could be other expenses. If you leave a camera on it consumes bandwidth. What you pay for with your ISP. Some ISP's have limits on how much you can use, some don't. Some have mechanisims in place which prohibit servers from being online unless you have a "business" class line. A true web cam includes a "web server" so you can access it remotely. You need to check with your ISP to see what the rules are concerning web cams and access to them if you want it to be "live" on the internet.
If you are just running it locally on your LAN then there is not any expense period (beyond the camera.)