The Gnome 3.x Activities Area
To run an application under Fedora (-or other Linux flavours using Gnome 3, such as Linux Mint), you first need to locate it! In order to do this, you need to enter the "Activities" area using one of the following methods:
- Clicking on the "Activities" link in the top left of the desktop
- Clicking on the "Super" key (-aka the Windows key) on your keyboard
Prior to Fedora 18, you clicked on the "Applications" button at the top of the screen, to display all the available applications.
From Fedora 18 onwards, you access this area by clicking on the following icon at the bottom of the Favourites area:

You should now see the "Applications Area" displayed:

If you can see the desired application, you can simply click it's icon to invoke it. However, it it often difficult to locate the exact application in such a large list, so Gnome 3 gives you two ways to narrow down the field:
By clicking on one of the predefined categories on the right hand side of the screen (-the default is "All") to narrow down the applications by their function. In the example below, the display has been limited to show just the installed graphics applications:

By clicking in the search box and typing in the name (-or part of the name) of the application; this will limit the display to those applications containing the string entered. In the example below, the string "ter" has been entered and Gnome has removed all applications except those with names or descriptions containing the string "ter" (e.g. terminal, Printers, Character map, etc):

Once you can see the desired application icon, simply click it to invoke the application.
Note: if you do not find the application you are looking for, then you will need to install it first
To switch windows under Gnome 3 you just need to click in that window. However, if you have lots of windows open, it may be difficult to locate the correct one. Gnome 3 helps you to find the desired window by entering the "Activities" area using one of the following methods:
Clicking on the "Activities" link in the top left of the desktop (-in Linux Mint this is an infinity icon - see the screenshot below)
Clicking on the "Super" key (-aka the Windows key) on your keyboard
Note: users of Fedora 17 and below will also need to click on the "Windows" button, once the "Activities Area" displays.
This will display thumbnails of all the currently open windows in the active workspace:

From here, just click on the thumbnail for the desired window to switch to it. If you wish to close a window without switching to it, hover the mouse near the top right hand corner: a white "x" in a black circle will display - just click this to close the window.