Re: extracting a still picture from a video clip in FC...
One of the most basic functions in FCPX. There are two ways actually. What you want is to place your playhead either with the Browser or Timeline active, go to the Share menu (the toolbar button or in the File menu (as of version 10.0.6), and look for the option to "Save Current Frame". This will allow you to export a still to your hard drive.
If you don't see it listed right away, then choose the "Add Destination" option. In there you can add it back to the menu. There are lots of options that are not in the menu by default and you can customized to your hearts content. This HUB article shows you how to customize the Share menu.
The second method, not what you asked for but I'll mention it anyway, is to create a still inside of FCPX. In a Timeline, place the playhead on the frame you want, use Shift-H to create a "Hold Frame".