If you're looking to only update your system and not looking for new software, you can use the more limited Update Manager, which only checks to see if there are newer versions of what you already have installed in the libraries.
Synaptic Package Manager
The Synaptic Package Manager includes a set of repositories through which you can search for software. You get to it by selecting System --> Administration --> Synaptic Package Manager. Click the Section button to see categories of software and then browse through what's available in the repositories. You can also do a search by clicking the Search button at the top of the page.
When you find the software you want to install, you click the box next to it, then select Mark for Installation and click Mark from the screen that appears. In some instances, the software you chose may require other software to be installed as well; if that's the case, you'll be told.
After you mark the software you want to install, you'll come to a screen that shows you all the software you've marked for installation. Click Apply at the top of the screen, and a screen appears asking if you want to "apply changes." (Linux sometimes uses the English language in a way that's only marginally associated with common usage.) Click Apply. The software will now be downloaded and installed. The Synaptic Package Manager will also install any software required to run the software you're downloading.
Want to uninstall the software? Again, it's simple to do. Run the Synaptic Package Manager, search for the software you've installed, click the box to the left of it and tell the Synaptic Package Manager to remove it. Then click Apply, and follow the same instructions for installing software. The Synaptic Package Manager takes care of the rest.
All this sounds simple, and sometimes it is. Unfortunately, though, sometimes there are glitches. For example, let's say you know of an application that you want to download that isn't listed in the Synaptic Package Manager. What do you do then?
Ideally, that application is in a repository somewhere, which just doesn't happen to be in the list of repositories in the Synaptic Package Manager. So you'll need to add the repository to the Synaptic Package Manager.
In some instances, the download page for the software will tell you which repository to use. Again, you'll need to know your Linux distribution, because different versions of the software for different distributions may be in different repositories.
To add the repository to your Package Manager, you select System -- Administration --> Software Sources, select the Third-Party Software tab, and click on Add. A screen appears, asking you to enter the "APT line" of the new repository. Again, if you're lucky, the software you want to download will have the exact line you need to add on its Web page. It may look something like this: