Well... if it doesn't necessarily have to have a cellular component... If you make it WiFi, it's a matter of a crappy IP Web Cam and a receiving screen. You would probably even be looking at something that only works on the same WiFi network.
If you want to build one that will work over cellular networks, then that's a no-go. First off, you're going to run into Cellular troubles, not to mention what you're doing would most likely be illegal (FCC).
With a WiFi model, there's a number of ways to do it, but finding an old Pocket PC (the iPaq 1910 would probably be ideal - small enough to fit, but powerful enough to display network video. You can get these on eBay for between $10 and $60.
Now, two issues: ONE - you need a program to display IP video on a PocketPC. There's a number of such programs out there and they shouldn't be too hard to find with a quick Google. TWO - You're going to have two WiFi signals in one box - one wireless web cam video, and one PPC serving as the monitor. This is the "out of the box" way to do it. Make sure there's a PocketPC software for your wireless webcam (it'll probably be web-based). Worst comes to worst, since it's an IP web cam, you will probably be able to stream the video through Windows Media Player Mobile.
It can be done, and you probably don't need a lot of electronics expertise to do it, but it's going to be costly and it won't look much like the Farnsworth - at least not the interface side.