This is where it becomes hard without seeing what you have. There are several different desktops that can be installed on Ubuntu and I don't use any of them. Everything I do is from the command line and I don't even allow the GUI to run. All I can tell you is look in unity or what ever menu system you have for a terminal application. It will give you a command line interface you can type in to. From there use the cd (change directory) and ls (list) commands to locate and go into the folder where you unzipped the server files. Then use the commands I gave you above to start the server.
There is also probably way of using the file browser to look at the properties of the ServerStart.sh and FTBInstall.sh files and mark them as executable. Then you should be able to run the ServerStart.sh from the file browser. But, as I said, I don't use the GUI so I'm not sure.