In Ubuntu, all components (applications, documentation, artwork, etc.) are split up into separate packages. Each package serves one purpose. For instance the package Firefox contains Mozilla Firefox, and Ubuntu-audio contains the Ubuntu default audio theme.
To install a program, select Applications > Add/Remove. When asked for a password, enter your login password. Select a category in the left pane. This corresponds to the Applications menu. Click an empty checkbox for any application you want in the upper right pane to select it for installation. Or deinstall an application by deselecting the application's checkbox. Nothing will actually happen until you click Apply or OK. A dialog box lists the pending changes, and if you click OK the required packages are downloaded and installed (or deinstalled if that's what you chose). When it's finished, click Close.
If you can't find what you're looking for, enter a word into the search box in the upper right corner. For instance if you enter "picture," it will show the GIMP, a powerful tool to edit pictures. You can also search for a specific application, such as Patience.
When you still can't find it, or you want to install a package not listed in Add/Remove, click the Advanced button. You can also open Synaptic by selecting System > Administration > Synaptic Package Manager. Enter your login password if prompted.
First click the Reload button on the toolbar to download the latest package lists. To search for a package, click Search on the toolbar. For example, enter "Tux Paint," and click Search. Successive search queries are stored in the left pane, and the results are shown in the right pane. To install a package, click the box to the left of the name. Select Mark for Installation from the list. Synaptic will warn when other packages (dependencies) have to be installed for the package you want to install. Click Mark to automatically mark the required packages for installation. The package you've selected is highlighted in green. Packages marked for removal appear in red. For Tux Paint, you see two other packages highlighted in green. Other required packages marked for installation do not appear in the search results for Tux Paint, because they are not specifically made for Tux Paint, and hence can also be used by other applications.
To browse for packages click Components in the lower left corner. The categories presented in the left pane are not corresponding to the Applications menu. The "universe" and "multiverse" categories hold packages not supported by Ubuntu. It is advisable only to install them if you know what you are doing.
When you have selected a package, a description is shown in the bottom pane. To obtain more detailed information (such as the download and installed size), click Properties on the toolbar.
When you are done marking packages, click Apply on the toolbar. This opens a dialog where you can see the pending changes. If you are sure, click Apply. The required packages are then downloaded and installed. When it's finished, click close.