I realise that this may be a very noob question but I accidently removed the the part of my taskbar that shows my current open applications and I can't seem to find any way to restore it. Is there any way to restore it back to the original settings so that I can see my open applications?

The applet you are searching for is called "Task Manager". Right click on an empty space on the Desktop and select "Add Applet". In the list that appears, find the Task Manager. Then drag it on to the panel.