I do this all the time. I am a schoolteacher and I have a master computer that I can do a demontration on, and all the kids computers in my computer lab will see my desktop on their screens and every action that I do. This type of software is very common to the education industry. You have to watch your costs as the software is typically licensed by the # of clients that you want to control. Look at AB tutor, I think it's a flat fee, $300.00 ??. I use an older but very adequate and functional one called Lan School Teacher, I forget the cost.... under $1000.000 for the whole lab maybe. It can blank screens to get their attention, you can remote control any computer while the kids are on and watching the actions, send messages, remotely restart, shutdown, logoff the computers etc. There is a free opensource one out there too. it's called LanView3 by MST software. I use that one mostly for it;s ability to do remotely wake up all the lab computers every morning (WOL). Wake on Lan.
There are limitations on how many computers you can send your desktop actions simultaneously to due to bandwidth used, but I can do 20 at once on our 100Mb lan. It gets sluggish at 30 and above.
Generally, you install software on the Master and then some client software on each computer you want to control. Not unlike a VNC setup. The better programs will allow you to do the client installs remotely, providing you have the client firewalls off or the firewall exceptions configured.
Good luck