The icons to the right of the start button are in what is called the 'Quick Launch' toolbar. To show this toolbar, you need to right-click an empty spot on the taskbar > mouse-over 'Toolbars' > select the 'Quick Launch' listing.
The quick launch will probably have a few icons there by default (at least one due to the 'Show Desktop' icon being a resident). Items of note on the quick launch toolbar:
1 - To resize the toolbar, right-click the taskbar and deselect the 'Lock the Taskbar' option. This will display a dotted bar which you can mouse-over and drag to expand the toolbar length allowing the adding and/or displaying of more icons.
2 - To add icons to the quick launch toolbar, you can drag them from the desktop onto the toolbar, or drag them from the relevant program's folder onto the toolbar. The taskbar needs to be unlocked for this action as well.
Note - if the taskbar doubles in height during the resizing of the quick launch toolbar, simply mouse-over the top edge of the taskbar and drag to the single size.
The icons at the top of the screenshot are part of a program offered by Stardock called "ObjectDock". You can find a link to the program under the 'Software' tab at the top of the page. There is a free version which you can use for one dock, and a paid version which offers multiple docks (both normal and with tabs). 
