Just launch the application you want to attach to the Unity Launcher or Ubuntu Dock; right click the icon and depending on your version of Ubuntu select the method below.

On Ubuntu 17.10 and later (with GNOME 3)

Select "Add to Favorites":

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Alternatively, click the "Show Applications" icon, browse to the icon of the program you want to add, right click the program icon and you will see the option "Add To Favorites". Selecting that option places the icon in the dock.

You can also drag applications directly from the Dash (or the 'Show Applications' list / 'Activities' overview) into the Ubuntu dock.

Before Ubuntu 17.10 (with Unity 7)

Select "Lock to Launcher":