To install new software in Ubuntu 14.04 you start by either clicking the Software center icon in the dock
Or you can search for it in the Dash and launch it from there.
If you know exactly the piece of software you are looking for you can search for it using the search field in the upper right hand corner. You can then click on the install button to install it.
As always when a new piece of software is being installed on the system you will be prompted to enter your user password to allow the install to begin.
Also by default new applications are automatically added to the dock. During the install process you will be shown a notification bar on top of the new package being installed showing you the progress of the installation process.
If you are unsure of what application you want to install you can search for it by browsing via category. Here we have clicked on the category Games. Here we can further dig into categories or by clicking on the double arrow view all 947 options in the Games category. Also you can view the Top Rated Games on this pane to see what other users have installed. The installation process is exactly the same here as it was via searching.
If you don't want new applications automatically added to the Dock on the the side of the screen you can click View and uncheck the New Applications in Launcher option to stop them from automatically being added to the dock.