Problem with moving corners of model


I am a beginner in Blender and I have small problem. I am trying to make a low poly penguin and I have already made it’s chest and feets. Now I want to form it’s body better by choosing all the points of a corner and moving it out, but this is what happens:

Instead of moving both right and left side of the corners, it just stretches it like tiny paper. I want it to make it like this guy made it (minute 6:55):

I hope you can help me out.

What you have are extra vertices. I’m guessing it was from an extrusion that you didn’t completely undo. You can either delete the extras, or merge them. Also, to try and avoid this, you can hit CTRL V and select “Remove Doubles”. As long as there are vertices overlapping, it will merge them (what I’ve seen anyway, I do the manual merge , ALT M, so I don’t have much experience with this method).