Windows Defender in Windows 8 has no support for right-click menus and therefore you cannot easily scan just a single file or folder. You can still run quick and full scans.
To launch Windows Defender, open Apps Search using keyboard shortcut Windows Key+Q, type "defender" into Search box and click the result.
Touch screen users should reveal Charms bar by swiping in from the right edge of screen and then tap/touch Search.
As Windows Defender updates its virus and spyware definitions only once a day by default, it is recommended to open Update tab and click Update first.
Those who have configured more frequent signature updates, can skip this step.
Running a monthly full anti-virus scan with Windows Defender in Windows 8
A full scan should be performed once every month to ensure that there are no viruses and malware hiding somewhere deep in your computer. You should also run a full virus scan when status of Windows Defender remains red after a quick scan.
Make sure Home tab is open. In the right part of the window click Full under Scan options. Then click Scan now.
Wait until the scan is complete (this might take several hours). Well, you can do some work if you have a fast computer, or you can call your friends or do some exercise... 
If everything's fine and status remains green, you can safely close Windows Defender window after the scan is complete.
Windows Defender lets you in case some malware has been detected - a yellow triangle with black exclamation mark appears with the warning. You must still wait until the scan completes to see details on the detected items.
If potential threats have been detected, Windows Defender will turn its status to red (for severe and high risk malware) or yellow-orange and present a big button named Clean PC after the scan is complete. Click that button to apply default actions right away.
You can also review detected items and select actions for these using the Show details link under the big red button.

If you chose to review all threats, a Windows Defender Alert window pops up. Here you can set action for each detection or use the Show details button to see threat description. After reviewing or making changes, click Apply actions.
If you clicked the Clean PC button, Windows Defender will apply default actions and present a list of removed malware. You can again use the Show details button for more detailed descriptions on selected item.
Click Close.
In some cases, a restart is required to remove all traces of malicious software. It is strongly recommended to reboot your PC right away in such situations.
Advanced usage - scan just one file or folder with Windows Defender in Windows 8
While Microsoft has removed Windows Defender context menu from Windows (File) Explorer, you can still use Command Prompt for scanning (and cleaning) just one folder or file. If you choose to scan a folder, all its subfolders will be scanned, too.
First, open Windows Explorer (Windows Key+E) and navigate to C:\Program Files\Windows Defender folder. Open File menu on Ribbon (if it is not visible, use keyboard shortcut Ctrl+F1), expand Open command prompt and click Open command prompt as administrator.
Click Yes in User Account Control. This will open the so-called Elevated Command Prompt in Windows Defender program folder.
Next, use Windows/File Explorer to navigate to the folder or file you want to scan. Hold down Shift key on keyboard and right-click the folder or file. Then click Copy as path. This will copy the full path to the item to Clipboard.
Now activate the Command Prompt window you opened earlier and type the following command: MpCmdRun -Scan -ScanType 3 -File. Add a space after "-File" and right-click in the window. Click Paste to add the copied path.
Press Enter key to launch the command.
The "-ScanType 3" tells Windows Defender to perform a custom scan. As you might remember from the Configure Windows Defender in Windows 8 article, "-ScanType 1" means a Quick scan and "-ScanType 2" means a Full scan. Only "3" allows using the additional "-File" switch for specifying a file or folder to scan for viruses and malware.
Please wait until the scan completes. If no malicious items were detected, the "Scanning found no threats" message is displayed.
If one or more threats were detected, Windows Defender will try to disinfect these. A usual pop-up notification (called Toast notification in Windows 8) appears on the top right of screen upon malware detection.
The "Cleaning finished" message should appear after threat removal is complete.

You can either close the Administrator Command Prompt window or run another custom scan. You can recall the last command by pressing the Arrow Up key (↑) - just delete the path after "-File" switch and paste a new path.
Making the scanning easier
If you need to perform manual scans frequently, you can create a special batch file on your Desktop.
Thank you Yugarian for the tip!
Open Start screen using Windows Key and type "notepad". Click the result.
Type (or copy & paste) the following lines:
@ECHO OFF
"C:\Program Files\Windows Defender\MpCmdRun.exe" -Scan -ScanType 3 -File %1
PAUSE
The first line turns off echoing (displaying) of each listed command. The "%1" in the end of the second line means the first supplied folder or file name. The third line causes Command Prompt to pause until user presses a key - otherwise the window will close automatically.
Now open File menu and click Save As.
First, select All Files (*.*) from the Save as type combo box. Then set a File name for the batch file - "Defender Scan.cmd" in this example. You can change the name as you like, but make sure you include the ".cmd" extension in the end, this makes the batch file executable.
Click Save.
Now you can drag any folder or file from File Explorer/Windows Explorer onto the batch file icon on Desktop and the item will be scanned.
Adding Windows Defender to Send To menu
To make on-demand scanning even easier, there is a trick to add the previously created batch file to users' Send To menu.
First, open File (Windows) Explorer. Then open View tab on Ribbon (if Ribbon is not visible, use keyboard shortcut Ctrl+F1) and make sure the Hidden items check box is ticked. This enables the displaying of hidden files and folders.
Second, copy the previously created batch file (Windows Defender.cmd) - right-click it and select Copy. Using keyboard shortcut Ctrl+C works equally well.
Third, back in File Explorer, locate and open C:\Users folder, double-click the subfolder with your user name and navigate to AppData\Roaming\Microsoft\Windows\SendTo subfolder.
For example, if your user name were Linus, the full path would be C:\Users\Linus\AppData\Roaming\Microsoft\Windows\SendTo.
Fourth, paste the batch file into the Send To folder using keyboard shortcut Ctrl+V or by right-clicking in an empty space and selecting Paste.
If you did everything correctly, the batch file is now available in Send To menu. Just right-click a file or folder, expand Send To menu and see if there is a Windows Defender.cmd (the name is different if you saved the batch file with some other name) entry.
In case there are other users on the same computer, you should copy the batch file to their SendTo folder also. Somehow, you cannot enable the scanning for all users at once by copying the file to same subfolder of the Default profile.