Looks like a high ISO shot from a consumer cam where the cam has really misjudged the settings. Image looks like it's been through noise ninja or some other noise reduction software.
Problems(some are already listed) --> Underexposed, handshake, settings were not controlled and rectified on the spot. Not using flash can give you a more natural result, but that does not mean you leave the flash off permanently in all situations. If that was the case, photogs. wouldn't spend 600++ on an external flash. In this case, flash would definitely have worked better, giving you a higher shutter speed and hence a smaller likelihood of blurred photos. Your photos turned out this way because the cam was likely using evaluative metering and the bright BG threw the meter completely off. If your camera has a center evaluative or a spot meter use that and meter on the face if you don't want to use a flash to fill in the subjects. Your hands look terribly shaky; it might be worthwhile to spend some $ on either a model with image stabilisation or a monopod/tripod.
WB is also off, resulting in that greenish cast. Try using custom white balance when the preset WB settings do not work.
The photos look terrible to be perfectly honest, I wonder why you didn't delete them on the spot. PS will not save these, for certain.