It is a nice way to install because you can see more information than in Ubuntu Software Center. It works more neatly as well.
At each start you are asked for the password, then it looks like that:
Search for the program to install or to see if already installed. You don't need to give the whole name, but a clue may help, for example for 'burning' software.
Those checked (green) are already installed. To install, uninstall and other options, right click an item.
An essential feature in Linux are 'repositories' - the source of software to be installed from the internet (programs you don't have on your computer to install, but that are installed through Synaptic Manager, Ubuntu Software Center, or the Terminal.) A lot of such repositories ('repos') are already there, but to install some new programs you may need new repos. To see, add or remove them, go to Software Sources (accessible in Applications Menu - Settings - or, in Synaptic Manger: Settings - Repositories, etc.)