I am a new Ubuntu user (migrating away from Microsoft/Windows) using Ubuntu 13.10. I like the feature of multiple workspaces. Currently, when I move between the four different workspaces, everything that I am doing in one of the workspaces follows me to the other. If I have LibreOffice up in one, the same documents are up in the other. Likewise, if I have a browser open, everything in that browser follows me to the other workspace. Is there a way to have each workspace be completely independent of the other? Thanks much for your answers!
I don't know how to do this on the standard desktop that comes with Ubuntu (although I'm sure someone else does) because I don't use it. But ...
This is Linux, which means that there's almost always more than one choice. You can use a different desktop manager (there are lots of them) or even have more than one at the same time and choose which one you want to use when you log on to your user account.
The KDE desktop manager has several features geared directly toward what you would like to do. Getting and installing it are not too difficult, but that's a separate topic.
What you are calling a "workspace" most likely corresponds to what is called a "virtual desktop".
In the simplest case, there is a task manager widget that you can add to your panel which shows what tasks are running on your desktop. It has an option which will display all tasks or only those which are on the current virtual desktop. You can define as many virtual desktops as you can manage. I use six. When you switch to another virtual desktop, the windows for the applications on that desktop are displayed and the ones from the previous desktop are hidden. However, the desktop itself with whatever you put on it like widgets and icons is identical to all the other virtual desktops.
If you want the whole enchilada, then KDE has a feature called Activities. When you (create and then) switch activities, you get a whole new set of virtual desktops which can be setup completely independently from those of another activity with whatever icons and widgets you want for that activity.
I have not used activities for a few years. They were a bit buggy back then, but I expect they are ready for prime time by now.
KDE also has a login option to remember and restore any applications that were running on your desktops the last time you logged in. That way, you don't have set things up every time you log in. You can choose to have it start fresh, restore what was there previously, or start a predetermined set of applications every time.