Export to wide screen (16:9) from Final Cut pro X
This answer assumes that the video that you're editing is already in a 16:9 ratio, otherwise when you export there will be black bars on the sides or above and below your video.

A 16:9 ratio is the standard for HDTV and Full HD. You're probably familiar with the Youtube video qualities - 360p, 480p, 720p, 1080p, etc. These are all 16:9. Therefore, all you have to do is export in one of these resolutions - 1080p is Full HD and 720p is HD.

For more reading on common aspect ratios, reference this Wikipedia page.