Let's face it, there are many situation where a standard network installation may not be feasible. Perhaps the walls are solid concrete or there is too much risk of hitting electrical/water lines to drill through unknown walls. Wireless may not be an option for a variety of reasons.
Most schools will in this situation staple network cables to the outside of the walls. Looks terrible and the staples may damage the cables, but it may be the only option. There may be another solution: send the network traffic over the electrical lines in your building. As long as all the wires are connected to a central system, data should be able to travel from any outlet to any other outlet.
The system behind computer networking over the local electrical system comes under the term "HomePlug." This is an unfortunate term in that it makes it sound like it is only good for a home. While a modern office building would not want such a system for a variety of reasons, an older school would be a prime canidate. The reason I say "local electrical system" is because there are a number of efforts -- mostly in Germany -- to put high-speed Internet over the power grid. There have been some experiments in the US, but the high number of transformers in the US electrical system makes networking over the power grid a bit of a technical problem. Europe apparently uses fewer transformers.
So will you get electrocuted by using this system? No more than you would plugging in your radio. The system uses the electrical system, but it does not use high voltages in its own operation. The system sends signals over the lines in such a way as to not interfere with the transmission of electricity. The only problem you may have is if your school has power equipment, such as a wood working room. Power tools may introduce enough noise on the line so as to make data transmission slow.
So how does powerline transmission compare with wireless? Powerline transmission is faster and is not constrained by physical objects -- walls, trees, hills, etc. The downside is that someone with a wireless laptop will not be able to sit on the park bench in front of the school. Also, most laptops come with wireless built in. The user would have to get an adapter for the powerline. In short, wireless is good for roaming around and powerline is good as a substitute for network cabling.
HomePlug Powerline Alliance -- HomePage