Q:

How to set up the Data Extract Activity to pick up a file from FTP Data Extract it and load the records into the Data Extension?

I have a scenario where the client will be dropping a file into their FTP, which I will need to pick up and load into ET's data extension.  
Currently the only available Extract Types in the Data Extract activity are Tracking Extract and Data Extension Extract.  

A:

Extracts are for getting data out of the Marketing Cloud.  What you would need to set up is an Import Activity, and a Custom File Location.
Creating File Locations

Go to the Email Application
Click the Admin tab on the navigation bar.
Under the Data Management tab, click File Locations. The File Locations workspace appears.
Click Create from the toolbar.
Select Location Type as "External FTP Site"

You don't need to set up the transfer that this page is detailing.  Just set up the location, and your import activity will grab the file from where you uploaded it.
Note: You cannot use subfolders in the file location. The FTP username must be chrooted to the specific folder you will upload the file to.  If you need subfolders, you would need additional FTP users, and File Locations set up in the Marketing Cloud.
Creating Import Activites

Go to the Email Application
Go to Interactions -> Import
Click Create from the toolbar.
Use your custom file location from previous step

Once these items are set up, you can then run your imports adhoc, or set up as part of an automation.

